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Synthetic Option Market Making
 
INTRODUCTION
Properly executed, synthetic option trades are virtually risk free and, therefore, represent the most risk conservative of all option trading. Synthetic trading is really a form of arbitrage, in which a discrepancy between the price of the actual option and its synthetic equivalent is captured as profit. Basic synthetic trading realizes an arbitrage profit in any same-month/same-strike call, put, and underlying asset.
Even if they are following other option strategies, option traders should be completely familiar with this form of trading, for synthetic principles will often determine which options are most appropriate for purchase or sale in any specific trading strategy. Trading synthetically does not require a fair-value option model, but such trading is almost uniformly impossible for off-floor option traders.
Synthetic arbitrage is based on the fact that a single-position long or short in any of the three trading instruments (call, put, asset) can be exactly duplicated by some combination of positions in the other two instruments. Any single long or short call, put, or asset contract position always has a synthetic equivalent value composed of a position in the other two option or asset contracts com­bined. The general put/call parity formula (Wong, 1991, p. 60) is:
P=C-S + DF(K)
Where    P =Price of put
C =  Price of call
S =  Current asset price
K =Strike price
DF( ) = Discounting function that calculates the net present value of the variable (in parentheses) at expiration
These parity relations are simplified for same-month and same- strike futures options in Table 5.1, disregarding for the moment the discounting function. Taking futures options as an example, a long call position is exactly equivalent to a long put of that same strike and a long futures contract, all of the same contract month. A long put and futures contract, therefore, is a long synthetic call. An option and its synthetic equivalent have not only the same delta payoff, but also the same gamma/kappa/theta risk profiles and, therefore, are risk-equivalent positions.
Table 5.1 Put/call/futures parity \1 X V (same-month/same-strike)
Long call= Long put and long future
Short call= Short put and short future
Long Put= Long call and short future
Short Put= Short call and long future
Long future= Long Call and short put
Short future= Short Call and long put
Conversing= Long future, short synthetic future
 (short call, long put)
= Short call, long synthetic call
(long put, long future)
= Long put, short synthetic put
(short call, long future)
Reversal = Short future, long synthetic future
(long call, short put)
= Long call, short synthetic call
(short put, short future)
=Short put, long synthetic put
(long call, short future)
Box= Conversion and reversal at different strikes
 
The strategy for trading synthetics is to take one side of an option position and the opposite side of its synthetic equivalent, so as to earn the price difference as profit. Knowing the price of any two same-strike/same-month options or futures, one can determine the price of the remaining option or future. These price relations between opposite options of the same strike/same month and underlying asset prices will be referred to as synthetic parity or equal value. Synthetic arbitrage takes advantage of differences in synthetic equal value prices.
Synthetic arbitrage is made up of conversions, reversals, or a combination of conversions and reversals known as boxes. Conversions and reversals are taken up in the next section and boxes in the subsequent section. For general illustration, the example of futures options will be used initially and then modified by consideration of financial asset discounts.
 
CONVERSIONS AND REVERSALS
A conversion is a long future, short call, long put position with all contracts at the same month (and strike). Equivalently, a conversion may be viewed as a long future/short synthetic future position, a short call/long synthetic call position, or a long put/short synthetic put position. A reversal (reverse conversion) is the exact opposite of the conversion: a short future, long call, and short put position. Thus, a holder of a conversion is always paired with a holder of reversal position.
A conversion or reversal is considered synthetically equal valued when the cost of the position is equal to the striking price of the options. For example, consider the following hypothetical prices: futures price at $104, a 100 call at $5 and a 100 put at $1 with all contracts of the same month. Since a conversion is a long future, short call, and long put, the cost of the conversion is $100 (= $104 $5+ $1). That is, the coat of the futures’ contract ($104) minus the sale of the call ($5) plus the cost of the put ($1) equals $100. Since $100 is identical to the option strike (100), this conversion is synthetically equal valued at these prices. The calculation of the reversal position will give the same result.
To verify quickly that these prices are synthetically equal valued, consider this situation: If a trader bought the 100 call for $5 and simultaneously sold the 100 put for $1 and the future for $104, then no matter where the futures price settles at expiration, the trader’s net profit will always be zero. Thus, if futures settle at 104, the trader will break even on the future contract, lose $1 on the time premium of the call (the call reflects only the intrinsic value of $4, not $5), and earn a profit of $1 on the 100 put as it expires worthless. The net result will be the same for any final futures settlement, not just 104, as one can easily verify with a quick calculation.
Procedures for computing synthetic equal values can be greatly simplified in practice. An in-the-money option should be synthetically equal valued to its same strike out-of-the money option when the time premium of the in-the-money option equals the time premium of the out-of-the-money option. In other words, option strike pairs are synthetically equal valued when the extrinsic, or time, value of each is the same. The only remaining difference in equal value between the strike pairs is intrinsic value.
Taking prices from the example above, one may quickly confirm this equivalence when futures are at 104:

	Extrinsic value	Intrinsic value	Total value
100 Call	$1	$4	$5
100 Put	$1	-	$1

 
When futures prices are at 104, the 100 call total value of $5 represents $4 of intrinsic value and $1 of extrinsic time value. The 100 put has no intrinsic value as an out-of-the-money option, but has $1 extrinsic time value. Since the time values of the call and put are identical ($1 = $1), they are synthetically equal valued to each other in this example. The steps in pricing the synthetic are summarized in Table 5.2.
When futures and options are synthetically equal valued (as in the above example) and can only be traded at those prices, then conversions and revei'wils offer no arbitrage profit. To obtain a synthetic profit, in the previous example, the option trader must either sell the 100 call above $5, or buy the 100 put below $1, or both, assuming that futures contracts can be bought and sold at exactly 104. A trader will attempt to buy the underpriced time value option or sell the overpriced time value option synthetically and earn the difference as profit.
Table 5.2 PriulnK the nynthetic
1     Calculate the intrinsic value (futures price - strike).
2     Set the out-of-the-money option price.
3     Add the intrinsic value to the out-of-the-money option price to find the same strike in-the-money option price.
Or
1     Follow Step 1 above.
2     Set the in-the-money option price.
3     Subtract the intrinsic value from the in-the-money option price to find the same strike out-of-the-money option price.
 
It is virtually impossible for a trader who is not on the trading floor to obtain synthetically profitable prices in option trades. This situation is not true for market makers. Not only must off-floor traders pay larger brokerage fees, but also, and more importantly, option prices need not be synthetically mispriced for floor market makers to earn arbitrage profits. Remember option prices are always quoted as either bid or offer prices. The average or settlement prices of options may be synthetically equal valued, but a market maker will always be buying somewhat below or selling somewhat above this exact equal-valued relation in the very course of making a market.
Using the example above in an actual option ring, one would find the 100 call is likely to be 4.90 bid at 5.10 offered, and the 100 put to be 0.90 bid and 1.10 offered. A trader could earn a maximum profit of 20 cents on a conversion or reversal by getting both sides of the edge on the put and call, (5.10 -5.00) + (1.00 -0.90), provided futures prices could be bought or sold exactly at 104.
Ideally, a market maker wishes to sell options slightly above and buy options slightly below synthetic equal value in the course of making a market. In the activity of earning liquidity function profits, the market maker can conveniently use conversions and reversals to reduce risk significantly.
To complicate this picture for a synthetic trader, the opportunity to buy or sell futures exactly at 104 cannot he taken for granted, and indeed, may become problematic. There are several reasons why executing the futures part of a conversion or a reversal may affect the profits of the synthetic trade.
First, option market makers often do not execute the futures side of option hedges directly but use brokers even in situations where they could trade futures for themselves. Option traders often avoid leaving the options ring in order not to miss important trades or because it is not easy to do so in densely packed crowds of traders.
In using floor brokers, however, option traders must almost certainly expect to give up the edge to futures market makers, and pay a small brokerage fee as well (about $2 per contract). If options are traded in bid/offer spreads, so are futures contracts. It is not always possible to buy or sell futures contracts at exactly 104. Perhaps they can only be sold at 103.95 or bought at 104.05.
Second, option market makers may face problems if the syn­thetic options trades are based on slightly out-of-date futures prices. Depending upon where an option ring is located, option traders may not always know the latest quotations in the futures ring and must rely on board quotations, which are of necessity slightly delayed.
Third, particular futures contract months are sometimes less frequently traded, and price quotations may be particularly unreliable. In these months, market makers may be forced to rely upon their knowledge of futures price time spreads to estimate a futures’ probable price.
All of these price-reporting delays and discrepancies can cause a market maker to misprice option synthetics slightly. Futures prices may be trading at 4.80 bid/4.90 offered and not the expected 4.90 bid/5.10 offered, at least not by the time an option trader wishes to complete the other side of a conversion or reversal in the futures ring.
To calculate the net profit owing to option arbitrage, one must subtract the cost of giving up the edge in the futures ring (in this example, 5¢), from the profit on both sides of the option trades (+20¢). If all goes well, then net profit is reduced but not eliminated. If futures prices are inaccurately assessed by option floor traders, then this arbitrage profit will be further reduced.
Option trndorH with a very large volume will often have clerks whose job is to signal futures pit prices directly to a trader before they are posted publicly, and if necessary these clerks give orders for market makers to brokers to execute futures trades. Although this up-to-date knowledge will reduce the loss from inaccurate futures prices when pricing synthetics, hiring a clerk will only be cost effective in large-volume markets.
Puts and calls do not always trade at exactly the same implied volatility. Sometimes a temporary market preference for calls in a rising market or puts in a falling market may send put and call prices out of line with their strike opposites. Contrarian technical traders may see this divergence as a barometer useful to predict a price direction contrary to the public market expectations. For whatever reason, however, wide disparities in the implied volatility levels of same-strike puts and calls mean that mispricing exists according to the synthetic parity formula.
If the market acts only from a directional sense in over- or undervaluing puts versus calls, the market is probably cheating itself by relying only on the purchase of one option and in so doing driving up time premiums relative to the other. A trader can always buy a synthetic put by buying a call and selling a future and obtain the same delta and kappa/vega risk. During a time of rising futures price trends, if the market is overvaluing calls relative to puts (or puts relative to calls in a falling market), an option market maker may take advantage of circumstances by selling the over-priced option and buying the underpriced synthetic equivalent. In this situation a general rule of thumb is to buy calls (and sell the synthetic) in a falling market, and to buy puts (and sell the synthetic) in a rising market.
A market maker must be totally familiar with trading synthetics and with the rule of value parity and risk equivalence between an option and its synthetic. If a trader is able to make quick calculations of synthetic price relations, he or she can earn a liquidity profit without knowing anything else about options. Even without a fair-value model (characteristic of markets before the BSM model) one can still trade and make a market in options using synthetic equivalence.
To simplify the repetitive calculations of the relative values of options and synthetics, market makers frequently have recourse to printed fair-value option tables that list the values of puts and calls over a range of futures prices with specified risk assumptions. With such a table the practiced trader can easily see at a glance which options are not trading exactly at equivalent fair values, or which options should be bought or sold. Table 5.3 is nn example of n fair-value option table.
 
Table 5.3      Fair value option table

Futures option value table	03-28-1991	Futures settlement = 100.00	©EPSILON	C Call value/Delta
Any May	Interest rate=10.00%	Days to expire=30	OPTIONS	P Put value \Delta
Valatility=15.0
Future strike

 
This basic principle of making conversions or reversals is the essence of synthetic trading. Synthetic option relationships offer the astute market maker frequent opportunities for small bid/offer spread and arbitrage profits. Unlike stock option synthetical trading, futures options need not consider the effect of dividends on synthetic trading. However, the discussion so far of trading conver­sions and reversals has assumed that there exist no costs of car­ry or capital opportunity costs. That is, interest rates are zero. Since this is not the case in the real financial world, we shall consider in the next section how interest rates affect synthetic arbitrage.
 
THE EFFECT OF INTEREST RATES ON SYNTHETIC TRADING
The BSM formula requires that interest rates be used to discount the option fair value in order to reflect the opportunity cost of capital, or the cost of carry. The specific relationship of cost of carry to option value varies depending on whether the underlying asset is a bond, stock, currency, spot commodity, or futures contract. Depending on the economic features of the underlying asset, the cost of carry will be either positive or negative, or even zero. For positive cost-of-carry assets, such as stocks, an increase in the interest or dividend rate will raise the value of the call and decrease the value of the same-strike put as the implicit forward stock price rises (see Cox and Rubinstein, 1985). In the bond market, both positive and negative cost-of-carry markets are possible, depending on the time spreading of a bond position relative to the term structure of interest rates (Bookstaber, 1987; Wong, 1991). In futures markets, where the current futures price is the forward price and contains the implicit cost of carry, option values are affected less by futures cost of carry than by the cost of carry of the option position itself. Option traders should be familiar with the cost-of-carry considerations in the underlying financial or commodity market in which they are trading. The following discussion of interest rates and synthetic values will be limited to futures options.
The fact that options must be positively or negatively discounted means also that the synthetic parity formula in the previous section will not nlwsyn hold before expiration. In other words, in actual market conditions options often do not trade at the pure synthetic basis because of different costs of carry of the option position itself. Synthetic trading is an interest-rate arbitrage as well as a put/call arbitrage.
The interest-rate arbitrage of synthetic trading extends to the financing of the futures option position itself, exclusive of the cost of carry of the underlying asset. When at- or near-the-money strike synthetics are traded, interest rates do not play much part in altering the synthetic parity formula. This lack of influence arises because the cost of carry will be almost the same for both sides of the strike. That is, to buy an at-the-money call and to sell the put will be done for even money.
The same is not true for wing strike synthetics, since on the wings there is a large difference in the cost of carry, with one option deeply in-the-money and the other out-of-the-money. Except for at-the-money conversions and reversals, one side or the other of a synthetic will always have a larger value and, thus, a larger absolute discount than the other. That one side of a synthetic has a larger value/discount than the other means that the parity formula must be discounted by the cost of carry to the buyer or seller.
Consider a situation where interest rates are 12 percent, futures are trading at 100, and the value of the 90 put is 0.50, or 50 cents, with 30 days to expiration. Without interest rates, the extrinsic value of the 90 put and 90 call must be equal, so that the 90 call would be worth 10.50 (10 intrinsic and 0.50 extrinsic). With a 12 percent annualized interest rate over one-month cost of carry (1 percent), the value of the 90 call would be reduced by 10.5 cents to approximately 10.40. This reduction will mean that the synthetic 90 put (call and future), will be worth only 40 cents. The synthetic put at 0.40 cents, therefore, is worth less than the actual 90 put trading at 0.50 cents. Generally, the out-of-the-money synthetic equivalent will almost always trade at some discount to the corresponding actual option.
The discount to the more expensive option in a synthetic position need not be the full cost of carry, however. For a synthetic position, the cost of carry is a function of the net debit/credit, not the debit/credit on the more expensive option alone. If the 90 put is selling for $4 when futures are at 100, then the synthetic parity value of the 90 call is $14 ($10 intrinsic and $4 extrinsic). The net debit/credit of the 90 synthetic (put and call), therefore, is just $10 and not $14. With a 1 percent one-month cost of carry, the 90 call will be discounted at 0.105 again, hut this time taken from $ 14. Thus, the synthetic value of the discounted 90 call should be about 13.90. That is, the synthetic 90 put should trade at $3.90 ($4 - $0.10), versus the actual 90 put at $4. In summary, the discount to the more expensive option in a synthetic trade is taken from the intrinsic value only, since the extrinsic value of both options in a synthetic will be equal.
From these discount relations, one can formulate a tactical goal of attempting to hold undervalued debit synthetics and sell overvalued credit synthetics, each value being determined relative to the cost of carry of the full synthetic position. The most nearly ideal situation would be to sell the in-the-money option at the full nondiscounted synthetic value and buy the actual option. By doing this, a trader will have established a net credit position that earns risk-free interest for the trader. Essentially, this goal entails doing in-the-money call and out-of-the-money put conversions and in-the-money put and out-of-the-money call reversals.
To pursue this strategy in the most prudent way, the smart trader is always on the lookout to keep a large inventory of long out-of-the-money options against which large synthetic credit trades may be made at any time. To attempt to leg the synthetic by selling the in-the-money option first, and then looking to buy the actuals may be too risky if for some reason the actual wings cannot be bought or become overpriced.
Although earning the interest rate on doing credit synthetics may seem like a small rate of return, the income so derived can be highly leveraged by the use of margin. Option margin is somewhat different on each commodity or futures exchange, but there is a tendency to accept the principles of delta margining. The process of delta option margining essentially uses net delta plus the number of options held to determine margin. The margin may sometimes be as low as several hundred dollars per option for synthetically spread options.
Since credit synthetics can usually be done for a net credit of many hundreds or thousands of dollars, the rate of interest on the synthetic credit may easily equal the margin in the best-case outcome. Thus, the rate of interest on the credit will not represent the true rate of return to capital, but will greatly underestimate it. For this reason, this net credit synthetic trading strategy is recommended whenever possible.
Nevertheless, even though a net credit synthetic position is a good strategy, it iH not perfect, For instance, deep in-the-money options do not trade so frequently as deep out-of-the-money options, and the number of synthetics that can be completed is thus limited. Also, although a net credit may be put on when doing a synthetic, it is possible that asset price moves may subsequently turn the net credit to a net debit with a negative cost of carry! This situation would develop if asset prices moved down against a conversion holder, or up for a reversal holder. In these cases, the positive cost of carry would become negative. This problem, how­ever, is overcome if a trader is able to execute a combination of conversions and reversals known as a box, discussed in the next section.
 
BOX ARBITRAGE
When a trader completes a conversion and a reversal for different strike pairs but of the same month, he or she has com­pleted a box. When a conversion (long future, short call X, long put X), is completed in conjunction with a diferent strike reversal (short future, long call Y, short put Y), only the net option position remains, because the long and short futures positions cancel each other out. Whereas conversions and reversals sep­arately always require some futures position, boxes do not (see Figure 5.1).

One-point spread price
Strikes
Figure 5.1 Put and call spread and box prices.
* Box prices assume single put and call prices. Other prices are based on one point strike spread. Futures = 100.
In doing boxes, it is appropriate to use any spread between the strikes of the conversion and reversal. A box may be done equally well on the 95-96 strike spread as on the 95-105 strike spread. Jellyrolls resemble boxes except that they are done horizontally in time, with a conversion/reversal in one month offset by a reversal/conversion in another month.
In looking for box trades, a market maker needs to be familiar with the vertical spread market for puts and calls. Spreads at the same strikes between puts and calls, when added, must equal the distance of the strikes. For a single whole point strike spread, for example, if the 100-101 put spread is trading for .55, then the 100-101 call spread will be equal valued at .45 with the synthetic box value summing to one point. In other words, knowing the value of an option spread of one option type, one can determine the synthetic spread fair value of the other option type for the same strikes.
An option trader should always be on the lookout for basic synthetic, box, or spread arbitrage profits. However, not all synthetic or box positions may be equally desirable. As we noted in the previous section, trading net credit synthetics offers a leveraged interest rate income in addition to normal scalping. For these reasons, all boxes should not be considered the same.
Ideally, a market maker trading synthetics as a net credit strategy would like to sell in-the-money options and buy out-of-the- money options. Practically, the trader must do conversions with deep in-the-money (short) calls and reversals with deep in-the- money (short) puts. By being long out-of-the-money calls and long out-of-the-money puts, a trader will show a credit balance on which interest may be earned. The optimum risk-free option position is to hold a conversion at strikes below futures price, and a reversal on strikes above future prices. This position will represent a net credit box spread. Obviously, the opposite position (doing reversals with in-the-money calls and conversions with in-the-money puts) is the least profitable synthetic strategy if the goal is to earn an interest income.
For a trader who is doing synthetics and attempting to create a balanced box, the number of futures contracts held long or short relative to the number of option contracts in the total synthetic position is a good indicator of the degree of balance for the box achieved. An optimum box, even one covering hundreds of contracts spread over all different strikes, need contain no futures contract positions in it at all.
 
PIN RISK
In a conversion, reversal, or box, the option trader is not subject to any of the major risks considered in Chapter 3 (skew, delta, kappa/vega or theta). Synthetics are virtually risk-free positions and, therefore, are generally considered the most conservative form of option trading.
Nevertheless, there are some risks associated with synthetic trading of which an option trader should be aware. Aside from the trading risk of completing synthetics, there is some very slight degree of rho risk since synthetic parity values will be affected by a change in interest rates as noted in the previous sections. There are two other risks that also deserve mention: expiration (pin) risk and inefficient market risk. Pin risk is taken up in this section and inefficient market risk in the next.
There are two forms of option exercise at expiration: futures/ asset and cash settled. Most options exercise a right to purchase or sell a futures/asset contract at or before the expiration date on the call/put (futures/asset-settled). The option and futures/asset do not have the same expiration, and the futures/asset continues to trade after the option expires. Thus, a May orange juice call is a right to buy a May futures contract up to the call’s expiration in April, while the May future continues to trade into May itself.
A cash-settled option expiration occurs when both the option and the futures/asset stop trading on the same expiration date and all cycle accounts are settled in cash differences. Since both expire on the same day, there is no longer a future/index contract for that month. Stock index options and stock index futures options (S&P 100; S&P futures and options, and so on), are the notable form of cash expiration on a quarterly basis (the triple witching hour). Stock index futures and options recently have introduced a form of futures-settled option expiration for off-quarter months. The December option is cash settled, but the January option is futures settled, for example.
From the standpoint of synthetic trading the most risk-free approach is a cash settlement option expiration, because there is no uncertainty about exercise if the underlying instrument expires in cash. Futures-settled or other financial options, however, carry Home risk at expiration. If futures settle near the exercise strike at expiration the opposite trader may not exercise the short side of the synthetic. This situation is known as pin risk, since h synthetic holder may be pinnel to the strike and future at expiration.
A long option holder may choose not to exercise at expiration even if the option is in-the-money. Consider a situation where futures settle at 100.20 on the last option-trading day and a trader holds long 100 calls. Will a long-call holder always exercise at this price? Not necessarily. Although the long-call holder will hold a call worth $0.20 in intrinsic value on expiration day, this profit may be realizable only if futures can be sold for 100.20. The critical unknown facing the long-option holder is how much the futures prices will change on the opening of trading on the next day after the expiration day settlement. In the above example, if futures prices should open below 100 on the next trad­ing day, then the profit on the long call will not be realized if exercised.
Since many off-floor option traders must pay a higher brokerage fee than floor traders and are not always constantly in touch with the market, some long-call holders will not exercise options that are in the money by only some small amount on expiration.
Somewhat paradoxically, a long-option holder may choose to exercise a slightly out-of-the-money option at expiration. Options do not have to be in-the-money to be exercised. This may be done, for example, if the holder wished to acquire the futures position without having to trade for futures in the futures pit. Taking delivery on futures contracts (long or short) via slightly out-of-the-money options may help large traders who, perhaps because of size or market liquidity considerations, wish to take a large position in futures without introducing new demand into the futures ring itself.
In summary, a long-option holder may not exercise a small in- the-money option at expiration if the profit is too small relative to the risk of futures price change at the opening of trade on the first post-expiration day. Also, a long-option holder may exercise slightly out-of-the-money options from time to time.
The problem that these uncertainties pose to synthetic traders with futures-settled exercise is the overnight uncertainty of then- actual position. Consider the situation where a market maker holds conversions at 100 (short 100 calls, long 100 puts, long fu­tures) when futures settle at 100.20 on expiration day. If the long 100 call option bolder exercises against the short 100 call market maker, then the market maker surrenders the long futures and carries no position on the day after expiration. But if the long 100 call trader does not exercise for some reason, then the market maker will carry over an unintended long futures position on the day after expiration.
Thus, the synthetic trader will not know whether he or she will be exercised against on the short side of the synthetic until after it is possible to do anything about it. This situation creates a period of time at expiration when there is risk exposure in a directional price move overnight. At expiration the synthetic holder of an at- or nearly in-the-money strike will be subject to windfall losses (or profits) from time to time.
Although one or two contract synthetics exposed to pin risk will not matter, having a large synthetic position at the strike closest to futures prices on expiration day poses an appreciable risk of unintended long or short futures carryover on the day after expiration for most market makers. Of course, there is also the possibility of windfall profits in futures-settled options, but this is always the other side of risk. A market maker will generally be interested in neutralizing risk, not speculating on it.
There is no perfect protection against pin risk in doing synthetics in futures-settled options. The most adventagous way to avoid this risk is to cross a conversion with a reversal of the same strike, and market makers may wish to check with other floor traders who want to get out of synthetics at expiration. Of course, finding a match is not always possible, and most market makers will often find themselves on the same side of the synthetic. Thus, the synthetic holder may be unable to avoid carrying pin risk into expiration.
In this situation, a market maker must make an educated guess about how many short small in-the-money options he or she will be exercised against. Although one might assume that all in-the-money options will be exercised at expiration, surprisingly this assumption is not always true. In practice, as much as half or even more of short options with small profit margins may not be exercised, but this percentage will obviously decline steeply as the option moves more into the money at expiration.
Expiration-related risk can only affect one option strike synthetic per expiration. Therefore, this risk will usually affect only a small percentage of a market maker’s total position, since rarely will a total position be at one strike. Although pin risk is not a catastrophic option risk, the absolute amount at risk may be high and worthy of attention.
 
INEFFICIENT MARKET RISK
A conversion or reversal is generally risk-free if the underlying call, put, and future are trading in a reasonably efficient market. Ideally, in an efficient market the relative synthetic fair values of synthetic options are priced within a bounded range. Practically, however, the same strike/month put and call may not trade at syn­thetic equal value equivalence. Such a market would be inefficient, and could pose some monetary risk to synthetic positions, at least until fair price relations came back into line.
The risk to the synthetic trader is that one side of the option synthetic will become drastically over- or undervalued in the absence of corrective market response. Although price inefficiencies are rare, they are not impossible. There are several ways in which such inefficiencies may affect synthetic option price relations.
Virtually all futures exchanges enforce some sort of limits on the maximum daily change in a futures contract (except possibly for the spot month near expiration). But not all exchanges have rules to limit daily price moves in options. Since a synthetic or reversal is composed of both options and a future, it is possible there will be times when synthetic price relations may not be synthetically fair valued on those exchanges with different limit restrictions on price changes in futures and options.
Consider a situation in a non-limit-restricted market where futures prices may fall from 100 to 96 on a given day. If there is a two-point daily price limit restriction imposed, futures prices will fall the limit to 98 and must settle there. If the option market continues to trade without limit, however, option prices may reflect actual futures market conditions and trade as if futures prices were at 96 (and not the 98 limit). In this situation, a large price distortion may appear in synthetic price relations. For example, assume that a trader holds a reversal (short futures, long calls, and short puts). If futures prices settle at the 98 limit, but option prices reflect futures prices of 96, the reversal holder will suffer a major loss at settlement, since his or her long call and short put have caused more losses than were matched by gains in the short futures. In effect, the gain on the real short futures does nol. offset the loss in the synthetic long future. Conversely, a conversion holder would experience a windfall profit in this example, equal to the loss of the reversal holder,
If the limit on a price move is on the order of $1000 per synthetic on an option exchange, then a large synthetic holder could be exposed to six-figure profit-and-loss swings on a limit day. Generally, reversal holders will suffer losses on downside futures limit days while conversion holders will show profits. On upside limit days, reversal holders may show windfall profits to conversion holder losses.
The losses on these synthetics (a reversal on a down limit day and a conversion on an up limit day) would only exist on paper, however, until the market came off limit (open trading re­sumed) and thus cannot be realized in any way. As long as futures prices eventually do come off limit, the losing side of the synthetic position will also eventually come out even again. Under no circumstances should a downside reversal and an upside conversion holder attempt to trade out of only one spread side of their positions, for there is no risk at expiration or when futures prices come off limit. To attempt to do otherwise is to risk locking in unnecessary losses.
A more serious risk for synthetic traders as well as others could come about in the event of a general market financial crisis, in which clearinghouses experience financial difficulties (see Chapter 3). A suspension of guarantees to an option trader that results in a forced liquidation of an option position can have serious financial consequences even to synthetic traders. If a trader believes that his or her clearinghouse is at risk of default, he or she should attempt to transfer (ex pit) his or her position to another house.

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