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世聯翻譯公司完成戰略介紹英文翻譯

On Strategy

INTRODUCTION

If synthetic trading may earn a good income and is the most secure and risk-free of any option strategy, why would a market maker attempt to trade in any other way? Probably the chief reason for trading nonsynthetically is that it is not always possible to trade synthetics in all markets at all times. More trading generally occurs in out-of-the-money strike options than in the corresponding in-the-money strike options. Thus, a trader is able to buy or sell an out-of-the-money call but finds there is virtually no open interest in the corresponding in-the-money strike put with which to complete a synthetic trade.

Even with at-the-money options in which both strike pairs trade more regularly, there may be times when both strike sides of a near- or at-the-money option either will not trade at all or will not trade in a manner that permits the market maker to effect a favorable synthetic trade. Low-volume option markets in particular will often fall into the latter category, although high-volume markets may offer a niche for synthetic-only traders.

For these reasons, a market maker willing to trade synthetically only will often find that many markets are simply unavailable, resulting in a loss of potential income. Thus, to trade more actively—indeed, to make a market regularly in most strikes at all times—a market maker must frequently trade nonsynthetically in order to trade at all.

For a market maker, trading nonsynthetically carries more risk. If a market maker’s nonsynthetic carryover position Ioses money, then the income earned market making may be wiped out. Market makers must perforce pay attention to nonsynthetic trading strategies, the risks they pose, and how to adjust and hedge positions.

When a market maker is not trading synthetically, the first decision he or she must make is to choose a strategy. There are about 20 basic single-month strategies and literally hundreds of possible time spread positions. Although earning the liquidity function profit of the bid/asked spread remains the overall goal of market making, what carryover position will be most appropriate? The ideal carryover strategy would (1) neither gain nor lose (especially lose) money over the long run, (2) allow the trader to keep net scalping profits, and (3) have a risk that minimizes bankruptcy and maximizes large payoff possibilities. Is there an optimum non¬synthetic carryover strategy for market making, and can it be executed?

If options truly have a fair value at trade prices, then theoretically the strategy used will make no difference whatsoever in profitability in the long run, since this is the definition of fair value. In other words, no option strategy is likely to have any different long-term payout than any other. But taking this theory at face value is to disregard preferences for risk. While either side of a futures or asset contract trade may have equal risk, all option strategies are not equal when measured from the standpoint of catastrophic risk or risk of bankruptcy.

Prudent market makers and dealers generally prefer limited- risk option (LRO) strategies over unlimited-risk option (URO) strategies as a means to minimize the risk of bankruptcy or default. A trader or firm can always lose some of its capital and then earn it back, but a person who loses his or her entire capital is out of the game. Specifically rejected as too risky from this standpoint are almost all short-time premium (positive theta, negative gamma/kappa/vega) strategies and many of the popular time spread strategies outlined in the previous chapter. An LRO trader who avoids these strategies sleeps more soundly and enjoys the weekends more than a URO trader.

In addition to the advantage of limited risk, many LRO strategies offer the possibilities oflnrge profits on occasion. The opposite of catastrophic loss is extraordinary profit, and of the two, large profit is better thim loss. Even if a market maker just breaks even on the LRO strategy over the long run, he or she will still attain the primary goal of keeping the liquidity function profits, which is the same objective as trading synthetics in the first place. But which LRO strategy should one pursue, and under what market conditions? This chapter attempts some answers to these questions.

One major difference between LRO strategies is that some have a delta directional bias and others are delta-neutral. The first section of this chapter discusses how technical analysis with trend predictive models may result in inconsistent success and how delta-neutral strategies are preferred. A delta neutral strategy allows the trader to earn non-trend-biased liquidity function profits and represents the profit for market making as a business.

The single-month positions that fit the conditions of both limited risk and delta neutrality are these: the long straddle/strangle, the long and short butterfly, and the long wrangle. The advantages and disadvantages of each will be presented in a subsequent section. These positions can also be used together in a time spread, which will be discussed in subsequent sections. The final portions of this chapter will consider how changing market conditions (broker order flow, fence markets, high-volatility periods and expiration) affect and change strategy.

DELTA (△) NEUTRALITY

For prudent market makers who wish to hedge risk and not speculate, delta neutrality is an important strategic goal. Strategies with a delta directional bias primarily interest option speculators who have opinions about market direction, whether based on technical or fundamental factors. Although market price prediction is not antithetical to or necessarily incompatible with market- making strategy, it is extraneous to it and often is not done well, resulting in losses.

There are several reasons market makers may wish to be delta neutral. First, speculative or directional strategies require the expenditure of time and effort in developing a technical or fundamental forecasting model of some sort, whereas market making is already a full-time trading activity. Since market makers need not have any opinion about the market to earn an income, some may find this added time and effort burdensome, or even distracting from the business of mnrket making, and prefer tobe delta neutral. Second, not having to worry about the direction of the market can confer considerable peace of mind to a trader.

What if the additional time and effort spent in forecasting prices bring additional profit, despite the accompanying psychological stress? No doubt for some this will be true. If a trader is able to predict the market successfully, then he or she will earn some speculative profit.

Earning liquidity function profits and earning a speculative profit are not mutually exclusive and indeed are the best of both possible worlds. Probably most market makers at one time or another have taken some speculative position in options, and often feel the allure of doing so again. Whether one can consistently earn money trading speculatively, however, is a much-debated question. Certainly, the popular do-it-yourself books on speculating promise high returns, but the empirical evidence is more equivocal. There are two approaches to speculating: those based on fundamental analysis of supply and demand and those involving a technical analysis of trading.

Fundamental Analysis as a Trading Strategy

Fundamental analysis is usually the purview of large informed capital interests, which have the means and commercial contacts to analyze fundamental data more accurately than anyone else. The large amount of capital that these informed interests control can move the market price in the direction of expectations, at least over the short run. Speculation based on fundamental analysis, therefore, may be considered the domain of the large informed capital interests. By its character, successful fundamental analysis excludes the majority of small nonindustry speculators from participation, since they have neither large capital nor inside or informed industry information about supply and demand conditions.

Technical Analysis as a Trading Strategy

Technical analysis, which (lutes from the nineteenth century, was developed to offer the small uninformed speculator the possibility of detecting the trading of large informed capital pools (smart money) and thus doing the same. Technicians assume (probably correctly) that large capital is usually right about price direction. When smart money is accumulating, it is time to buy, and when smart money is liquidating or distributing to the public, it is time to sell.

Since large capital is thought to be on the other side of small (public) capital in the accumulation/distribution cycle, some speculators adopt a contrarian perspective: Do the opposite of what the public is perceived to be doing. When all public speculators have bought (or sold) at the bullish peaks (and bearish troughs) there is no money left to push the market, and prices will reverse—as smart money was betting.

In classical technical analysis such as is found in Edwards and Magee (1957), price alone is deceptive in trying to identify large informed money interests, since price is often used by large capital pools as a smoke screen to lure unwary traders into taking incorrect bullish or bearish positions. Properly done, technical analysis relies upon price as a speculative guide only in conjunction with volume analysis. Classical technical analysis is really volume analysis, since the hidden tracks of large informed speculators are left in the trail of the volume of trading activity.

For a classical technical trader, a head and shoulders price formation, for example, must be confirmed in volume analysis. Thus, early technica was synonymous with tape reading, that is, deciphering the individual price and volume transaction records. Modern technical analysis now uses price and volume data to suggest that it is still possible to earn consistent speculative profits. By identifying where smart money is trading against the public, technical traders try to do what smart money is doing, and ride on its coattails to profit.

As with any form of advertising, it is “caveat emptor” about the claims made for technical analysis. While some individual traders have demonstrated their ability to earn large fortunes speculating, at least for some periods of time, many of these same traders have ended up losing most if not all of their capital if they continued to trade. It is not widely known, for example, that one of the legendary technically oriented traders, Jesse Livermore, ended his life as a bankrupt suicide. Livermore made and lost several million-dollar stakes before giving up (Sarnoff, 1967).

Setting aside anecdotal evidence, however, studies have shown that most speculators are not right and do not make money on average over the long run (Teweles and Jones, 1987). Some studies show as few as one in four speculators earning money over many years, and other studies show less success than this. Speculation is indeed risky.

Although most speculators lose money, studies also show that some, mostly large, speculators may do well consistently for many years (Maddala and Yoo, 1990). Large speculators appear to make money although there are fewer money makers than money losers. If we ignore commercial hedging profits/losses, we see that the speculative profit of the small group of large traders in effect comes at the expense of the cumulative losses of the large majority of small speculative traders.

The evidence suggesting that the majority of traders consistently lose money at the expense of a smaller number of larger traders is consistent with the premises of technical analysis. What the evidence does not confirm, however, is whether the technical analysis method of trading is able to improve the success rate of most speculators. For example one popular technically oriented stock forecasting model (the “Wall Street Week” Elves) was dropped from that program after completely failing to anticipate either of the stock market crashes of 1987 or 1989. The Hulber Digest, which tracks the trading records of many of the most popular technical trading advisories, has shown that many, if not most, overstate the success of their speculative trading results and that few consistently make money in all types of markets. The few large public commodity funds, which usually use technically oriented trading strategies, also do not appear to do well consistently when tracked over long periods of time, confiming the poor results of technically oriented speculation (see The Wall Street Journal, Jan. 28, 1991). Although technical analysis promises great financial suc¬cess, the record suggests that most speculators will not be successful if they are undercapitalized with inadequate information, whatever method they use.

Most speculators lose money over the long run, and small technically oriented traders are likely to be losers. Although there are some successful large speculators, the overall odds are against small speculators, which most market makers would be if they speculated. In light of this situation, delta-neutrality is the appropriate strategy. Whether futures prices go up or down, delta neutrality assures the market maker a profit.

Floor traders who have traded speculatively and then attempt to become market maker have to give up thinking in terms of market direction. Remember, the object of any successful trader is to make money, not to be proved right. Market direction is only a means to an end, not an end in itself.

Summary

Regardless of the added work, since empirical studies have shown that most speculators are wrong and lose money, speculating in delta-directional strategies will often be a waste of time and money. For these reasons, risk-averse market makers will want to avoid speculative strategies generally, even if they have limited risk, and remain delta neutral. Of course, this rule is observed universally in the breach by taking shots once in a while, and seasoned market judgment may also recommend a non-delta-neutral strategy from time to time, provided the extra risks are understood.

CORE STRATEGY

Since different market participants may have different overall strategic goals, there is no such thing as the optimum option position for all risk tastes. For market makers qua dealers only, however, there will be a preference for limited nonspeculative (delta-neutral) risk strategies. Aside from synthetics, there are only four single-month positions that fit this limited-risk, delta- neutral (LRO-DN) profile: the long straddle/strangle, the long and short butterfly/condor, and the long wrangle. Each of these strate¬gies will be reviewed and considered for relative advantages or disadvantages. The reader may wish to review the profit/loss and risk profiles of option positions in the Appendix to Chapter 4. Generally, the long butterfly/condor and long wrangle strategies are preferable to the short butterfly/condor and long straddle/strangle strategies for single-month positions. Time strategy will be considered in the next section.

Long Straddle/Strangle

The long straddle is an LRO-DN strategy that earns money in the event of wide futures price swings or increases in implied volatility (kappa/vega). Although a straddle will earn monoy with strong price moves in either direction, one can also make monoy with the long straddle by trading futures against the trend on large price-swing days. Since the straddle gets longer delta as futures prices rise and shorter delta as they fall, large swing days will earn profit, especially if adjustments are made at price turning points intraday. This trading strategy is known as trading gamma, which will be discussed more fully in Chapter 8. A long straddle holder will also earn additional profits if implied volatility levels increase greatly. If a wide futures price move and an increase in implied levels occur simultaneously, the profits to a long straddle holder can be substantial.

Some traders hold a long volatility philosophy of option trading, which says the long straddle is the optimum strategy. Despite its advantages, however, the long straddle strategy suffers from some serious weaknesses. The chief disadvantages of the long straddle are the high cost in negative theta risk (time premium decay against the trader) and the risk that volatility will not increase and may even fall. In the worst case, the combination of both, futures prices do not move and implied levels fall. A market maker who is long kappa/vega will attempt to continue to earn liquidity function profits to offset losses from time decay or minor falls in implied volatility, but a trader cannot always accomplish this and may take temporary and possibly large losses.

Although the long straddle is a delta-neutral strategy, it is not really a kappa/vega neutral strategy, and its losses, although limited, can be quite high if kappa/vega moves in the wrong direction. In extreme cases a sharp drop in implied volatilities from relatively high levels may approach or exceed catastrophic risk from the short side. Of all the LRO-DN strategies, the long straddle strategy is the most exposed to catastrophic kappa/vega risk in certain (high-volatility) market conditions.

Aside from risk considerations, market makers rarely hold pure straddles for the simple reason that making a two-sideil market means that one will almost always be long and short options at the same time. The long straddle/strangle is probably the least desirable LRO-DN strategy both theoretically and practically for an active market maker.

Long Butterfly/Condor

The long butterfly/condor is the only LRO-DN strategy that is positive theta, at leant some of the time. By being short more time premium in the center options against long time premium on the wings, the long butterfly is short premium and will earn some time decay profits so long as the butterfly remains centered at the futures price.

As we noted in Chapter 4, one of the risks associated with being positive theta is being negative gamma and kappa/vega in single-month positions. For the butterfly, however, the negative kappa/vega risk is contained by the protection that the butterfly wings afford should futures prices move off center by a large amount. Although the long butterfly is positive theta in the center, kappa/vega is neutralized at the price extremes. If the market remains in a period of low volatility, a butterfly earns a small time decay profit, without the catastrophic risk of the short straddle strategy. Because of the costs of neutralizing kappa/vega, theta is less positive than the short straddle, and thus less profit is earned. The long butterfly/condor is really the only prudent short time premium strategy and is sometimes termed a limited risk credit spread.

Short/Butterfly Condor

In the short butterfly, the limited risks of the long butterfly are inverted; that is, negative theta and positive kappa/vega if futures prices remain unchanged but positive theta and negative kappa/vega if futures prices move sharply in either direction. To lose money to time decay in quiet markets but have only limited profits in volatile markets is not a desirable strategy, given the actual volatility of asset or futures prices. In effect, the short but¬terfly/condor has all the disadvantages of the long straddle without any of its real potential to earn catastrophic profits. Long butterfly strategies are preferable to short butterflies.

Long Wrangle

The long wrangle is an LRO-DN strategy that resembles the long straddle in attempting to profit from high real and implied volatilities but without the drawbacks of the long straddle/strangle with high negative theta. In effect, the long wrangle attempts to neutralize the disadvantages of the long straddle but retain its long volatility risk profile.

The long wrangle strategy essentially utilizes the credit from the sale of center strike options to purchase a greater number of out-of-the-money options. When done carefully, the long wrangle position can usually be put on at a credit and, therefore, is a limited-risk credit spread. By being short time premium in a credit spread, the long wrangle has a low negative-to-neutral (and sometimes even positive) theta at the center strikes, much like a long butterfly.

Although neutral theta in the center, the long wrangle will maintain a positive gamma and kappa/vega in the wing strikes. By remaining long positive kappa/vega, the long wrangle strategy may permit a trader to gamma trade when necessary, and benefit from a large upward move in implied volatility if futures move in either direction. Although it is not possible to be positive theta, positive gamma, and positive kappa/vega at the same time in the same single-month position, it is possible to do this in the same position over a range of strikes, which is what the long wrangle does in its trimodality of risk. It is this trimodality that makes the long wrangle a very versatile LRO-DN position for single¬month strategies and closely relates it to the favorable trimodal risk profile of the long butterfly.

Despite the advantages of long wrangles, however, as complex ratio spreads they are particularly sensitive to skew risk. Skew risk in the vertical spread implied volatilities will generally affect all the delta-neutral limited-risk strategies. The positive (or negative) skew in put and call strike slopes will make wing strikes more (or less) expensive relative to at-the-money strikes. For example, in establishing long butterfly/wrangle carryover positions, a market maker is sometimes selling lower volatility (center) options and buying higher implied volatility (wing) options. However, the effect of skew risk is generally not fatal to the viability of long ratio strategies, although it will be discussed again in Chapter 8.

Comparison of Single-Month LRO-DN Strategies

The optimum single-month option strategy would be exposed to limited delta, positive theta, and positive kappa/vega risks. Such an option position would earn a premium time decay profit while also earning profit on futures price swings. A theoretically perfect option position would earn a profit no matter what happens to real and impliod volatility levels. Unfortunately, the theoretically perfect option position is impossible for single-month positions.

The two credit-spread LRO-DN strategies considered above— long butterfly and long wrangle—each have one advantage of the optimum position, and also one disadvantage, since it is never possible to be positive both theta and kappa/vega simultaneously in a single-month position. The butterfly attempts to maintain a slight positive theta in the center but incurs small losses on the wings. The wrangle attempts to participate in a positive kappa/vega stance on the wings, while neutralizing theta in the center.

Generally, the long butterfly/wrangle strategies are positive or neutral theta in the center and neutral or positive kappa/vega on the wings; that is, they are both trimodal in risk. Because of their trimodality of risk, the long butterfly and wrangle strategies are probably the most appropriate stances to assume if the actual probability of futures price change is semilog normal. The long but¬terfly and wrangle positions will be positive-to-neutral theta during 68 percent of the time that futures price change occurs around the mean price (that is, plus or minus one standard deviation). The rest of the time, these positions will become neutral-to-positive kappa/vega when futures prices blow out. In the financial markets the appropriateness of trimodal risk positions for actual market conditions is suggested by the deviations from log-normality of asset prices. These also represent a trimodal error curve (see Figure 2.5).

In summary, market makers have a preference for limited-risk non-price-speculative strategies, among which the long butterfly/condor and the long wrangle positions are generally the most favorable for single-month strategies. The long straddle/condor position is too kappa/vega risky as well as being impractical for an active market maker, while the long butterfly is preferable to the short butterfly because of the likely real risk. Market-making positions with trimodal risk profiles are consistent with the trimodality of the deviations from normal theory found in market data.

TIME SPREADING

Time spreading improves the core single-month limited-risk delta- neutral strategies. Disregarding the straddle, there are nine combinations of two-legged horizontal spreads between the short/long butterfly and long wrangle single-month positions only. Are any of those time spreads preferable to others?

As contracts move into front-month status (with less than a month to expiration), selling the center strike options short is often popular with large institutional, commercial, or speculative traders. Such naked short selling in the front month, whether commercially hedged or not, tries to capture the most time decay profit. This situation creates net selling from the public to market makers, who then may become much too long kappa/vega. The strategic goal of the front-month position, therefore, should be to minimize negative theta risk and, if possible, to be slightly positive theta. The long butterfly is the only LRO-DN strategy that allows a trader to do this, and for this reason a long butterfly position may normally be considered the prudent market-making strategy for the front-month leg of any time spread.

Likewise, there is no point in holding positive theta (short pre¬mium) positions in the back months, where theta risk is low and time premium decay minimal. Rather, it would be better to be positive kappa/vega and participate in a futures price blowout or implied explosion, which may generate catastrophic profits. For these reasons, the long wrangle strategy may be preferred for back- month positions.

If one combines these desirable single-month strategies, a limited risk delta-neutral time strategy emerges that holds a long butterfly in the front month and a long wrangle in the back month. An example of such a time position is illustrated in Figure 7.1 using a 30 to 60 day futures option time spread and its payoff at expiration, with futures basis at zero, interest rates at 10%, and implied volatility at 15%. The positions are constructed using the long butterfly and long wrangle in the appendix to Chapter 4.

At 30 days before front-month expiration, the payoff of this time position resembles a long straddle, but by front-month expiration resembles the payoff of a long wrangle, with its characteristic W shape and trimodal risk profile. Time kappa/vega is positive on both the put and call out-of-the money wings, but negative in the center strikes. Time delta is either neutral or even slightly positive in the center strikes, but negative on the out-of-the-money wings. Time delta is not a serious risk if it is properly hedged with offsetting futures spreads, but time kappa/vega risk must always be evaluated with concern. However, the trimodality of the time kappa/vega risk for a long wrangle must be considered limited. The maximum negative risk, about seven cents for a minimum 10-contract timo spread of this nature, is not large and is less than half the maximum risk of the short Iront/long back strategy.

Futures

Figure 7.1 A time strategy. Error curve smoothed and fitted from Figure 2.5. Expiration refers to front-month option.

Moreover, the trimodality of risk allows this time position to become long time kappa/vega risk on either wing, which restricts risk while removing limits on profits. Generally, there is a long gnmma/kappa/vega profile overall that may be actively gamma traded. The baHic carryover posit ion yields long delta on the upside and Hhort delta on the downside, letting profits run, Should implied levels increase greatly in a futures price move, the time strategy will earn additional profits as a windfall. This combination of long gamma and long time kappa/vega .gives the long butterfly/long wrangle time strategy its wallop.

Adding at least one back-month leg in a time butterfly would lend variation and some flexibility to the combinations of time spreads possible. With a time butterfly, it would be possible to carry for a limited time a short or negative kappa/vega single-month leg. From the standpoint of overall time strategy, however, nothing will change significantly from the risk/reward characteristics of the two-legged time spread if proper weighting has been achieved. Although the optimum strategies for all traders are likely to be somewhat different, depending upon market conditions and overall goals, the above position may be considered the basic workhorse of prudent time strategy for market makers.

Despite it advantages, there are some disadvantages to this time strategy that should be underscored. Skew risk in such a strategy becomes particularly important for any large ratio spread position, although it is in general still limited. Skew risk will be taken up again in Chapter 8.

Any long ratio spread will also be subject to catastrophic risk after an extremely large increase in implied levels, profitable as these may be. The only market condition that presents an unlimited risk to long ratio spreads is a high implied volatility level, which can fall precipitously. Although long ratio spread strategies may be the most profitable in the move from normal to high levels of volatility, they may also be among the most unprofitable in the move from high to normal volatility. This topic also will be reconsidered in Chapter 8.

Managing a time spread effectively over time requires atten¬tion to actual market conditions and to handling expiration dates and cycle rollovers successfully in order to maintain the time spread balance (a cycle rollover is a change in positions from one cycle to the next). A time spread is always changing as back months become front months, front months expire, and new months begin trading. A market maker is generally rolling over his or her time spreads constantly as one cycle expires and others begin; such rollovers may be made more or less difficult by market conditions. Issues related to expiration will be taken up later in this chapter.

Options usually do not trade in butterflies or wrangles outright. These complex strategies must be implemented separately by active trading, legging the component spreads in the total position. To some extent the actual supply and demand for options, by different strike and month, will determine how easy or difficult it is to maintain this core strategy. The supply and demand for options, which is essentially the net broker order flow, initiates most option trades.

BROKER ORDER FLOW AND OPEN INTEREST ANALYSIS

Any preferred strategy must be tested against market conditions and modified accordingly when conditions change. Among the most important market supply-and-demand conditions are broker order flows for options. Broker order flow becomes critically important in determining the ease of implementing complex option strategies.

Broker net order flow is simply the change in net balance of buying or selling by brokers of each option by strike and month. Since as much as 90 percent of all option trading is initiated by brokers and not market makers, the net balance of public orders is more important than the volume per se in ferreting out the supply- and-demand forces in the market. Open interest, the outstanding (existing) option contracts by cycle and strike, shows the result of broker order flows. Broker order flows and open interest will define fairly clearly a market’s supply-and-demand structure.

Open interest is neither long nor short, since an open interest of one contract is always a buyer paired with a seller. As each day’s trading is completed, the open interest is either subject to change, or not. \blume can raise or lower open interest, or leave it unchanged. If both sides of the trade are new initiators, then open interest increases. If one side is a new initiator and the other a liquidator, then open interest does not change. If both sides are liquidating existing positions, then the open interest declines. A market maker will want to know not only who initiated a trade, but how open interest was affected.

What is relevant in open interest is not only the size but also the side of the initiator of the original trade, and how these affect open interest change. Most trading in an option pit takes place between market makers and brokers, but it is the brokers who almost always initiate the order. Have brokers been not Hollers or buyers of options? In which month and which strike? Are they putting on new positions or liquidating? Knowing who is buying or selling, and which market participants hold what option positions, can give a market maker an edge in knowing how to price option bid/offer spreads.

Broker order flow and open interest analysis are fairly easy, depending upon the size of the option pit (that is, the number of floor traders and brokers). The smaller the pit, the easier it is to follow order flows and open interest changes completely. In small pits (less than a dozen traders and brokers) determining order flow and open interest are almost an exact science if one is willing to do considerable work. In large pits of 40 or more traders, net broker order flow cannot be easily observed by any one trader in the pit, for large pits tend to fragment into smaller trading networks (Baker, 1984). Without an accurate gauge of net order flow, open interest changes will become less meaningful.

Nevertheless, a trader should learn to do this type of analysis as much as possible in any size pit. Following broker order flows in conjunction with open interest ideally gives an astute market maker information about the likely positions of most of the option trading market participants—that is, commercials or speculators (the public) and market makers (the pit)—what they are trying to do, and what strategy or pricing tactics are appropriate.

An option cycle begins up to a year or more before an expiration day. Since market open interest will be initiated by broker orders, the beginning of each option cycle starts with a broker net order flow (that is, the broker-initiated buying or selling of a specific contract or spread). For each cycle there are, as a practical matter, only five broker net order flow situations for single-month cycles. These are:

1 Equilibrium of supply and demand

2 Net buying of calls and puts (long volatility)

3 Net selling of calls and puts (short volatility)

4 Net buying of calls and selling of puts of different strikes (bull fence)

5 Net selling of calln and buying of puts of different strikes (bear fence)

An equilibrium in net broker order flow is probably the most favorable with respect to a market maker, since risk may be easily hedged with core strategy or outright synthetics. Less favorable are the other four market conditions, which require some strategy modification. Any long-volatility strategy will suffer some losses in the event of a persistent selling of options by the public, espe¬cially as expiration approaches. A short-volatility net broker order flow will limit the total position a market maker is able to carry. A long-volatility net broker order flow, however, may well bring unex¬pected profits to market-maker carryover positions; and this flow is favorable to core strategy up to a point. Long-volatility net order flows will eventually lead to high implied volatility prices, which may result occasionally in catastrophic profits for market-makers. (These topics will be further discussed later in this chapter.) Two other nonequilibrium conditions may be reflected in bull or bear fences in net order flow. Fences are used as an effective inventory hedge by commercials and often have the advantage of not incurring a debit since there is a sale and a purchase of options.

Consider the hypothetical beginning of an option cycle with heavy broker-initiated selling of out-of-the-money calls, light selling of at-the-money calls, heavy buying of at-the-money puts, and light selling of out-of-the-money puts (see Table 7.1). In this example, the predominant broker order flow is toward establishing a bearish fence for strikes above at-the-money, along with some other selling of out-of-the-money puts. Since the public, through brokers, is establishing a bearish fence, the pit will be doing the opposite side of the transaction as a bullish fence. Trading fences exclusively will present market makers with particular risk prob¬lems, which are discussed later in this chapter.

Table 7.1 Broker net order flows and open interest (single-month)

Strike Calls Puts

High

At-the-money 1000a

(heavy

selling)

100 1000 a

(light

selling) (heavy

buying) BEAR

FENCE

Low 500

(light

selling)

a Indlicates large open interest

The broker net order flow may and does change over the course of an options life cycle, or even daily or hourly. Yet in many option pits, the trend of broker net order flow will often last for several weeks or months. It is important to identify these trends, for they are a key component in strategy.

The supply-and-demand forces for each option cycle may be followed by keeping a small notebook with the above market open interest conditions laid out, although with experience market makers may carry this information in their heads. An example of such record-keeping for broker order flows is presented in Table 7.2. From this schematic of current broker net order flows and open interest figures, it is possible to begin to estimate the entire public market position and trading activity and goals. In Table 7.2 one may see that brokers and the public are buying a bear fence in the back month, buying a bull fence in the middle month, and going short volatility in the front month. To interpret how these current broker order flows are related to existing positions it is necessary to follow the changes in open interest over several months.

At the beginning of each new option cycle, the broker order flow will quickly build up an initial open interest, since both sides of the trade (public and market makers) are establishing new positions.

Table 7.2 Broker order flows by contract month

Month Front Middle Back

Strike Call Put Call Put Call Put

High

At-the-money

Low H-

*H- *H-

*L- O

*H+ 0

H- *L—

*H- L- *H+

Key:

H Heavy Activity

L Light activity

O Little trading (no broker bid/offer)

- Broker net selling

+ Broker net buying

* High open interest

The predominant broker order flow will define the predominant open interest position directly in the back-month trading.

It is probably safest to begin any new position at the start of a cycle with long options or prudent spreads. If this proves difficult or untimely to execute to any size, then a net order flow is prob¬ably buying options and making them scarce. Correspondingly, if it becomes easy to buy options but difficult to sell them, then net order flow is selling options. Without equilibrium, a market maker will have some difficulty from the beginning in executing the legs or spreads necessary for prudent strategy.

When the transition is made from the back month to the middle month, one of two things may happen. Either broker order flow remains the same, or it changes to another of the five broker order flow types.

Let us consider the first case: Broker order flow in the middle month period remains the same as in the back month period. Under these circumstances open interest may continue to increase, or it may at some point become static. If open interest does not increase, any new trading is divided equally among those establishing new positions and those liquidating old ones. If open inter¬est continues to increase, then accumulation will be occurring in both the back and the middle months. It is unlikely, however, that open interest would decline without a shift in broker order flow, since the pit and the public would not be changing sides; that is, liquidation could not occur without some change in broker order flow.

In the second case, a shift in broker order flow occurs. If open interest increases as a result, then new sections of the public and floor traders alike are establishing new positions. If open interest does not change, then the pit is probably shifting the risk of the different option positions held in open interest from one section of the public to another. If open interest falls, however, then the public has now begun to liquidate the positions it had already established.

In either case, market makers are looking for fundamental shifts in demand (accumulation) and supply (liquidation) for options, as expressed through the open interest and broker order flows. There must always be some accumulation in open interest at the beginning, but there need not be liquidation before expiration.

Over the life cycle of an option contract from back to front month, an option strike will first go through a stage of accumulation, as reflected by one of the five broker order flow con-ditions. These initial broker order flows may continue until expi¬ration or change one or more times before then.

It is useful to have some strategic perspective on market structure. The general goal of safe market making is to establish a limited-risk option carryover position around which to make a market. Broker order flows, however, sometimes make this possible only to a limited extent; and market makers must think ahead to see what kinds of orders are most desirable or most likely to be possible.

Although the specific sequences that broker order flows may go through from beginning to end cannot be known in advance, a trader following market structure over time will have some idea where pressure on prices is coming from and how this pressure is effecting implied volatility change. A market maker should try to price competitively in the direction of the broker order flows over time, and look for options to trade strategically that will provide good spreads or time legs for limited-risk market-maker positions.

Generally a market maker will attempt to analyze open interest changes as a means of identifying the participants in the day’s trading and interpreting what the future direction of supply and demand may be. By tallying an ongoing record of trades and open interest by strike, a market maker tries to ascertain the holders of the supply and demand for all option contracts. When distressed liquidation, overoptimistic buying or acute speculative buying by the public becomes apparent, a market maker will wish to adjust bid/offer spreads rapidly.

It is difficult to specify explicitly how the different combinations of broker net order flows in each of the option contract months and their changes will affect strategy in complex time spreads. Following broker order flows and strike open interest is sometimes an arduous and protracted affair in which perfection is impossi¬ble. The trader may expect some modest success in pits where he or she can generally observe most of the trading during the day. The chances for success are less in larger pits or under conditions of screen (upstairs) trading, where too much trading is going on simultaneously or is not available on a reporting system (for ex¬ample, over-the-counter markets).

Nevertheless, following broker order flows as much as possible is a good trading strategy and may easily be worth the extra effort. The next two sections will deal with two important broker order (low market conditions; fences and high-volatility periods.

TRADING FENCES

In option markets it is not uncommon for the public to do explicit or implicit fences, forcing market makers to take the other side on balance. A fence-driven market, especially in smaller option markets, may make it harder for market makers to maintain delta neutrality or even to be positive or neutral kappa/vega. An option trader should be familiar with trading and adjusting option fences, since these may be the dominant trade in broker net order flow for periods of time.

There are two broker net order flow fences: a bear and a bull (Figure 7.2). A bear fence is a short call/long put and a bull fence is a long call/short put, where the options are of different strikes. Fence option strategies are commonly used by commercials who wish to hedge spot prices for one reason or another. For example, a commercial who is long inventory or futures will buy a bear fence in options for protection or hedge against spot inventory price declines. In this case, the bear fence with the long future or inventory will equal a vertical bull spread. Fences are particularly attractive for commercial hedgers since, if the cost of the option purchased is equal to or less than the cost of the option sold, the fence can be established without a debit other than basic margin.

Bull Fence

Short Future

Futures price

*=fence option strikes

Figure 7.2 Bull and bear fence expiration payoff and with futures,

Fences pose special problems to market makers since the short option wing of the fence is exposed to unlimited delta and kappa/vega risks. To be prudent, market makers must hedge both these risks, thus closing the fence. The key unhedged option in a fence is the short side option. Additional trades in futures, options, or some combination of both will neutralize the short side risk and close the fence.

Five ways to close the fence to unlimited risk exposure are discussed below, along with the disadvantages of each.

1 Use futures to establish a vertical spread. The simplest way to close a fence is to take a position in the assets market that is the opposite direction of the fence. Holders of bear fences will buy assets and bull fence holders will sell assets. The resulting position is either a bull or a bear vertical spread (which mirrors the opposite position of the commer¬cial hedgers with inventory).

2 Although spreading the fence will curtail the unlimited risk from the short option (by doing in effect a covered write), the resulting position will not be delta-neutral. Also, since only futures have been used to hedge the short option, there remains some (limited) risk of kappa/vega exposure. Although the total spread-adjusted fence will not be net short options, the option that is short will be of a different type from the long option and probably of a wide strike difference. If there is a wide implied volatility skew difference between the wings of the fence, a market maker will still be exposed to some possibly severe financial risk from kappa/vega risk. Because a futures/asset adjusted fence is not delta-neutral and has some kappa/vega risk, closing a fence with futures offsets is not the best response to these market conditions although it is acceptable if it is the only alternative possible, as sometimes it is.

2 Synthesize the short option. Synthesizing the short option, by buying the opposite side of the same strike and hedging with futures, will leave the trader with a simple long net option position. The trader will now hold a conversion or reversal at the strike of the short option, and the original long option of the fence will be held alone. Of course, if both strikes of the fence were synthesized (by doing the opposite side of the fence with another fence with opposite side options), a box would result, one of the lowest-risk option positions.

Unfortunately, if there is a persistent broker order flow on one side of the fence, boxing the fence is rarely possible. Even synthesizing on the short side alone is not always possible.

3 Buy different strike options on the short side of the fence and adjust with futures (step spreading/ratio spreading). Buying more of the short side options of a different strike will effectively reduce the unlimited-risk wing of the fence by spreading. If a trader buys a higher strike option of the same type that is short, the resulting position will be a vertical step spread in the short direction and an open long position in the other direction. If a trader buys a lower strike option of the same type that is short, a ratio spread will be created in the direction of the original long option of the fence.

However, if the broker net orders are persistently trading a particular fence, there may be few options of the short side available with which to create these favorable spreads and close the fence.

4 Buy more of the long side options of different strike (convert to long ratio spread). Buying more of the long side of the fence, and using futures to offset the short option side, can also close the fence. Unlike the other situations, when brokers are trading fences heavily, the long side option often may be obtained cheaply because brokers are attempting to leg the fence separately, or are willing to trade ratio spreads. If the fence can be closed by buying more of the long side op¬tions, the result will be a long ratio spread in the direction of the long options.

Ah with spreading the fence using futures only, buying more of the long side options alone will leave the trader without any long options of the short side type for protection in the event of an upside blowout in the implied volatility skew. However, since the trader is now net long options, there is greater protection than if a fence were closed using futures alone. Also, by buying more of the long option side of the fence, a market maker may more easily obtain delta neutrality for the near future.

5 Time spread. Time spreading may also close the fence. However, offsetting a fence in one month with a position in another month exposes the total position to new time risks that must be considered, as seen in Chapter 6.

These are the main ways to close a fence, although other more complex spread or time trades may also work. Unfortunately, many ways of closing the spread have attendant difficulties. Using futures alone to spread the fence leaves the market maker exposed to some skew volatility risk, and a futures-adjusted fence also is not a delta-neutral position. Synthesizing the fence is, of course, the optimum from the standpoint of risk, but it is often impractical or impossible. Vertically spreading the short option side will also close the spread, but in case heavy broker net order flow is doing only one direction of the fence, getting long the short option side may prove difficult, especially in smaller, less liquid pits.

Buying more of the long side of the fence and adjusting with futures (going long a ratio spread) will often be most nearly opti¬mum from the standpoint of risk, cost, and market conditions. By heavier weighting on the long option side, one can also neutralize delta over the short run. The disadvantage of this means of closing the fence is that the trader becomes excessively long kappa/vega on the long option side (as is most of the rest of the pit) and will not be delta-neutral near expiration. Nevertheless, this situation will be a limited risk that can be adjusted.

Time spreading, of course, may be used to close a single-month fence in different ways. A second fence in a different cycle could be used to close a fence in another month; if this time spread was a bull and bear fence, then the total risk of the position would In-considerably reduced and would have the advantage of being dell n neutral as well. Nevertheless, this spread position would eventually face the problem of rolling over or ending at expiration. The risk from holding fences in one month may also be offset by other time leg positions, a topic taken up in the tactics of time spreading (Chapter 8).

TRADING HIGH VOLATILITY

If one takes long periods of historical and implied volatility into account, the volatility of asset and futures markets separates into two groups: There are periods when the ranges in volatility are relatively normal, and there are periods when they are extremely high. For many commodity futures and options markets, the normal range (based on long-term historical averages) may be considered as anywhere from 10 to about 25. High ranges can be anywhere from 25 to the high 100s, and these appear suddenly, without warning from immediately preceding prices. Of course, each asset or futures option market has its own normal and high volatility ranges (for example, see Figure 7.3). High-volatility shocks rarely last more than a half year before normal long-term averages are restored. Normal ranges of historical and implied volatility are characteristic of market conditions about 75 to 80 percent of the time, with high volatility characterizing the rest of the time.

Soybean Futures

Corn Futures

Figure 7.3 Implied volatilities of soybean and corn futures: Nearby series (October 1, 1986-September 30, 1988). (Source: Chicago Hoard of Trade, Commodity Futures Professional, January 1989.)

High-volatility periods offer the prospect of larger market- maker profits in several ways. For example, high trading volume often accompanies high-volatility periods, and the increased trading is good for normal business. Also, the higher volatility of the underlying asset will tend to widen the bid/asked spread in a dealer market, leading to a higher (potential) gross profit.

High-volatility periods also offer the promise of larger profits if the strategy has been designed—with a long gamma and kappa/vega risk stance—to maximize position profits at these times. Indeed, it is during periods of high volatility that the long kappa/vega time strategy comes into its owri, and market makers may participate in very large profits. For the other traders who have assumed unlimited risks, times of high volatility bring great danger and risk of financial catastrophe.

Going into a high-volatility period, there are two main ways a trader derives profit from a long kappa/vega strategy: from the delta or gamma profits that are a result of widely fluctuating asset or futures prices; and from the potential for an increase in the implied volatility level.

In the first case, profits will accrue as asset prices move in one direction or another because the long kappa/vega strategy is also long gamma. Knowing if and when to take this profit, wholly or in part, is the essence of gamma trading. If the asset price continues to run strongly in one direction after the initial volatility shock, then very large profits will continue to be earned. Should asset prices move sharply backward in a reversal, these same profits can disappear rapidly. In a market of high volatility, frequent asset price reversals, and whipsaws, capturing profits may be easier if delta-neutrality is re-established more frequently.

A compromise tactic would probably take advantage of both ways to gamma trade and lock in some profits from any initial volatility shock price move. A long volatility position would want to lock in at least some profit from large asset price moves to be prudent, but still let some profits run.

In the second case, profit will result if implied volatility levels increase along with the change in asset volatility. Implied levels are likely to respond upward, even if only to reflect higher asset volatility, especially if the change was unexpected. However, if large sections of the market are caught holding short kappa/vega positions in the initial volatility shock, there may he a secondary shock in implied levels when a short squeeze develops among the negative kappa/vega traders who are weakly capitalized and vulnerable to exploding margin and clearinghouse requirements. In effect, a short squeeze will often develop after a sudden increase in historical volatility, which will then push option prices (and implied volatilities) even higher. Short covering negative kappa/vega traders will frequently push option prices (and volatilities) extraordinarily high, as few remain who are financially able (or willing) to sell options to those covering their short positions. An example of this short squeeze and implied volatility blowout took place during the stock market crash of 1987 when short out-of-the-money stock futures calls actually rose in price, reflecting implied volatility levels as high as 140 despite a 500-point drop in the Dow Jones Industrial Average!

Whether one is net long or short options ultimately determines whether one experiences catastrophic profits or losses in a move from normal to high real or implied volatility levels. If the long volatility strategy earns the most profit in high volatility periods, the negative kappa/vega strategy will often be financially devastated by high real or implied volatility. This situation is probably the most common cause of option trader blowouts. Even if a trader is short only $1,000 kappa/vega, he or she could suffer a $100,000 loss if implied volatility suddenly increased 100 points, as happened in 1987 and again in 1989. If one option trader’s gain is another’s loss, it is better to be on the side of the gainer in these normal- to high-volatility transitions, which is why prudent strategy remains neutral or positive kappa/vega during periods of normal implied volatility levels.

Despite the advantages of an initial long kappa/vega risk stance, some dangers that are inherent in this strategy must be understood and rectified when appropriate. A long kappa/vega position is best situated in a volatility explosion, but it is not necessarily the best situated once high volatility has peaked. Trading during periods of high volatility requires special attention to new and dangerous risks. It is one thing to make money on the increase in volatil¬ities from 20 to 80, but another to give it all back, and more, as volatilities go from 80 to 20! Sooner or later high market prices and implied volatility levels will drop, sometimes even in the face of an extremely large futures price move; for example, the spike in crude oil implied volatilities on January 24, 1989, and January 16-17, 1991, which rose to an implied volatility level of 150 in one case, only to crash to 50 overnight, even with a large percentage drop in futures prices.

Like the wise gamma trader coping with an extraordinary rise in real volatility levels, the positive kappa/vega trader should lock in some (ultimately) large portion of profits by selling options and attempting to reduce the long kappa/vega exposure. A large positive kappa/vega will reward the trader with large profits in the transi¬tion to high-volatility periods, but once in a high-volatility period, a positive kappa/vega risk becomes catastrophically exposed and must be prudently lowered. It is during high-volatility periods that even a long kappa/vega trader may inadvertently suffer serious financial difficulties if he or she remains large positive kappa/vega too long. For this reason the volatility risk exposure of a market maker’s carryover position should be hedged by selling options to achieve some degree of kappa/vega neutrality. These sales will lock in market-maker profits without further market risk.

Sometimes, when asset prices become more volatile, the implied volatility level of options may stay the same or even drop! There are several reasons why asset prices and option volatilities may not move in the same direction together. It is possible that the total market already holds low-risk offsetting positions and that there /is no large group of short kappa/vega speculators caught short and needing to cover—possible, but not always likely. An inversion between market prices and implied volatility levels would also signal the market’s opinion that the increase in market volatility is temporary and will soon collapse. For whatever reason, however, an implied volatility/market inversion in a high- volatility period is likely to be financially disastrous to a heavily long volatility strategy. Although such a strategy is low risk, it is not no risk; an inversion is perhaps the largest risk event that this strategy will experience. Long ratio or wrangle strategies will be particularly exposed to inversion risk since the ratio structure of the position risks going into a falling implied volatility period at the same time that the position gets longer volatility.

To offset the potential loss from the inversion of the implied levels, the long volatility strategy expects to earn profit from the gamma trading or the run in delta. It is possible that losses from a collapse in implied levels may be greater than the profits from gamma, in which cuho the position would show an overall loss.

Because implied volatility may drop in the event of an increase in asset price volatility, the long ratio volatility strategies are not without some major financial risk under some market conditions.

Consider a real situation, in which asset prices went from $40 to $20 in one month, a 50 percent drop, yet implied volatility dropped from 150 to 40 at the same time; this happened on the oil option market of the New York Mercantile Exchange in the first few months of 1991. Under such conditions a trader holding a long bear ratio put spread would have gained some gamma profit as prices slid 50 percent, but would also have suffered some losses due to the collapse of implied volatility. Indeed, it is not impossible that the losses on kappa/vega risk would be larger than the profits from the asset price move in this situation.

A condition in which sharply lower asset prices lead to a drop in implied levels may be more characteristic of commodity markets rather than other option markets. Sharply lower stock prices in 1987 and 1989, for example, were accompanied by sharply higher implied levels, proving profitable to the long ratio put holder.

Given these possibilities, prudent strategy will seek to understand the different market and implied volatility relations in the specific market being traded. A prudent strategy may attempt to weight the wings differently in a delta-neutral butterfly/wrangle position, in the direction of the appropriate price movement up or down, to take into account the possibility of an implied level inversion to high market asset price volatility.

As a final note, implied levels may temporarily trade at different levels from high real volatility if there is a limit restriction on futures price change in one day but not on option prices. In such a case, option implied levels based on limit futures prices will not accurately reflect true market conditions. For example, assume futures prices are at 100 and a constant option implied level of 10. If futures prices should make a limit move of 2 points to 102, and there are no price limits on options, then the formula for implied volatilities based on the limit price (102) will be inaccurate if options are reflecting a higher futures price. If implicit as if futures are trading at 104 instead of 102, then calls will be overvalued and puts undervalued using a 102 futures price in determining implied levels. In these market situations, true implied levels are likely to fall between the implied levels of puts and calls and would be the put and call average.

Conversely, with the average put and call implieds, one can compute as if futures prices based on option synthetic prices. For example, if after the limit move of futures from 100 to 102 the true implied level remained at 10 (despite calls settling at 12 and puts at 8), then market makers would immediately be able to determine the as if futures price based on postlimit market synthetic put/call prices.

Market makers will always know what the as if futures prices are, and even the contango or backwardation in the futures time spread, based on fair-value option sheets. With knowledge of as if prices, futures options market makers can continue to make market and trade options, provided they take care not to violate any of the risk prudence of the core strategies. Even if future prices have moved the limit, market makers can continue to trade gamma using options trades. With care, the potential profits remain large.

EXPIRATION

Incorporating the inevitability of expiration into a trading strategy requires skillful management of changing option risk. As middle- month positions turn into front- and near-expiration-month positions, kappa/vega risk is greatly diminishing, but gamma and theta risks are growing rapidly. The drift in delta may become quite severe in nonsymmetrical positions as standard deviation shrinks on a daily basis. At this time a trader often must pay spe¬cial attention to position adjustment if he or she is not holding a synthetic position.

For the long butterfly, delta adjustment near expiration is somewhat like trying to balance a ball on the end of a pointed stick. The large negative gamma means that a trader will be buying or selling futures, or delta, in the direction of the market more frequently, and consequently suffering more frequent whipsaw losses. The compensation is higher positive theta and time decay profits near expiration, but it often seems to the short premium trader that the time decay profits do not cover the gamma adjustment losses. If n trader minimizes gamma adjustment to avoid whipsaw losses, the market may seem to choose that very time to make a big trend move in one direction or the other.

For the long straddle or wrangle trader, the situation is just the opposite. Positive gamma means that no adjustment is required in the event of a futures price move, and consequently there is no risk of whipsaw losses. But the long extrinsic value of the position is decreasing rapidly. If futures do not move in price, the long straddle/wrangle trader may suffer net losses despite gamma trading if negative theta becomes greater.

It is also true that many positions carried near to expiration begin to display quirky risk features if the distance between the component strikes is too wide. As noted previously, a long butterfly is considered a limited-risk option position because the short center straddle is theoretically risk-hedged by the long strangle on the wings. This protection, however, will work only if the strike spreads are close enough in standard deviations to be meaningful. Near to expiration, if the wings are several standard deviation points (say, five or six) away from the center strikes, then scant protection may be provided in the event of a large futures price move. Long wrangles will also begin to take on the risk profile of short straddles near expiration if the out-of-the-money strikes are too many standard deviations away from the center and futures remain in the center. Generally, a large option position will begin to shrink its risk profile to that of the options with strikes closest to where futures prices are trading. This change may alter the real dollar risk to the position.

To avoid many of these problems of severe risk drift and quirkiness, an option trader should run hypothetical at-expiration profit- and-loss risk profiles of large positions by month beginning several months before expiration. Doing so will allow a preview of special or large expiration risks that a trader may wish to correct before expiration arrives.

For traders with long kappa/vega positions in the back and middle months, the approach of front-month status will require some changes in strategy. Generally, a trader does not want to go into front-month status too long kappa/vega, in the event that short premium sellers may force down prices to expiration. Yet the limited-risk trader does not wish to go short kappa/vega and join the short premium sellers either. From day 45 to about day 30, therefore, it is advisable to adjust to only moderately long kappa/vega. During this time a trader should look for spreads that will reduce quirky risk features of option positions being held.

When the front month becomes one month or less, a trader may wish to consider synthesizing as many spreads as possible into conversions or reversals. Synthesizing an option position in effect “lands” a position safely at expiration with the minimum amount of risk and is recommended for risk-averse market makers. Generally, large open or nonsynthetic option positions should not be carried into the expiration week or day if it is possible to avoid them.

In Chapter 5 we noted that even synthesized option positions will carry expiration risks if assets or futures prices are trading at or near the synthetic strikes at the cycle close. This is known as pin risk. That is, the trader risks being pinned to the strike on the short option side. As a result, the trader suffers overnight uncertainty about whether he or she will be exercised against and about how many futures to carry overnight. An incorrect judgment about futures carryover may mean that the trader is not delta neutral on the morning opening after exercise and will suffer large windfall losses (or profits).

For these reasons, a market in trading at-the-money strike syn¬thetics sometimes will develop at or near expiration as traders attempt to avoid pin risk. Traders holding synthetics will try if possible to liquidate with other traders holding the opposite side of the synthetic (conversion or reversal). These trades are usually done at fair value with no profit for either trader. Since the pit has often been on the same side taking public orders, however, liquidating synthetics without loss is not always possible except in limited instances. When the pit is mostly on one side of a synthetic, at-the-money synthetics will trade at a slight premium for the added expiration risk.

It is lore among floor option traders that futures prices tend to gravitate at expiration to the option strike with the largest open interest. Of course, it is always possible that this is the perception of all people who fear the outcome for themselves if they happen to be holding part of that largest open interest strike. As we shall see, there may be some market justification for this popular belief.

By no means all option traders will be holding synthetics at the near-expiration strike. Since we have already seen that the gamma of a near-strike option will be greatly increased near expiration, in practice an option trader who wishes to remain delta-neutral will be making frequent adjustments. Whenever futures prices trade above or below the strike in question, however, the adjustments required for nn at-the-money option at expiration will he reversed. For example, a short call holder will attempt to buy futures if futures prices rise above the strike and sell futures if they drop below the strike. Of course, the long call holders will be attempting to do the opposite to remain delta-neutral. Thus, for the holders of non-synthetic at-the-money options near expiration, futures prices rising above or falling below the at-the-money strike will produce a flurry of trading adjustments that will send futures prices gyrating above and below the at-the-money strike. This phenomenon grows especially noticeable on the very last day of option trading before expiration.

If this explanation is a fair description of the adjustments that many traders undertake near expiration, then the strike with the largest open interest will also have the largest number of traders making adjustments when futures are above or below this strike and, thus, the largest impact on futures prices at this time. It is quite possible, therefore, that the strike with the largest open interest near expiration will be drawing futures prices up or down to this strike as part of the adjustment strategies peculiar to expira¬tion. Futures prices may gravitate toward the largest open interest strike for these reasons, confirming market perceptions.

Expiration risk also includes the risk of early exercise or assignment of options. For underlying asset markets where forward price is not always taken into account in the option itself (unlike futures options and markets), the present value of future value or forward price must be implicitly derived before determining the pre-expiration exercise value of an American option. In the case of futures options, however, the desirability of early exercise to the long option holder may directly be determined and will be considered for illustration.

Generally, a long futures option should be exercised when the cost of carry becomes equal to or greater than the value of the corresponding strike pair option. If a trader exercises when the cost of carry is less than the value of the strike pair option, then he or she would give the value of the difference to the short option assignee as a windfall profit. If a trader does not exercise a long option when its cost of carry becomes greater than the value of the strike pair option, then the nonexerciser has also given a profit to the short option holder that equals this difference.

The following simplified example may make this clear. Assume the following prices and values with 30 days to expiration:

Futures price =100

90 put=0.20

Interest=12 percent annum

From the synthetic parity formula, the fair value of the 90 call in the above example would equal intrinsic value (10.00) plus the value of the 90 put (0.20), discounted by the cost of carry for one month. The cost of carry for an option synthetically valued at 10.20 would be 0.102 for one month. Since the cost of carry is less than the value of the corresponding strike pair put, the long 90 call holder would not wish to exercise. If the market value of the 90 put were 0.05 rather than 0.20, however, then the long call holder would wish to exercise to avoid excess costs of carry.

It may be seen from the foregoing that the risk of early exercise or assignment to the short futures option holder is not large. If the long option holder exercises too early—before the cost of carry is above the value of the strike pair option—then the short option trader in effect gains the long option at a discount. If the long option holder fails to exercise after the cost of carry is above the strike pair option, then the short option trader is earning a premium interest on his or her net credit position.

Early exercise is not really much of a risk, but in fact, will almost always work to the market maker’s advantage in futures options markets. In the cash option market, early exercise may present a somewhat different situation, which must be examined more carefully based on the cost of carry of the underlying financial asset and its forward price.

cents for h Hitiglo option, oh in $2.50 bid for the 100 call. The

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