Chapter 9 Risk Considerations

Chapter 9 Risk Considerations
第九章 风险考量

Consider the prices and theoretical values shown in Figure 9-1. What categories of volatility spreads might be profitable under these conditions? By comparing prices to theoretical values, or by comparing the implied volatilities of the various options to the volatility input of 15%, we can see that all options are overpriced. Recalling the general guidelines in the last chapter, under the given conditions a trader will want to consider spreads with a negative vega:

Call and Put Ratio Vertical Spreads
Short Straddles and Strangles
Long Butterflies
Short Time Spreads

Which of these categories is likely to represent the best spreading opportunity? And within each category, which specific spread might be best?

参考图 9-1 中的价格和理论值。在这些条件下，哪些类别的波动性价差可能获利？通过将价格与理论值进行对比，或将各期权的隐含波动率与 15% 的波动率输入进行比较，可以看出所有期权都被高估。回想上一章的指导方针，在这种情况下，交易者应优先考虑负 Vega 的价差策略：

看涨和看跌比例垂直价差
卖出跨式和宽跨式价差
买入蝶式价差
卖出时间价差

这些类别中哪种更可能提供最佳价差机会？在每个类别中，具体哪种价差可能最优？

CHOOSING THE BEST SPREAD
选择最佳价差

For the moment, let's focus on May options only. Having eliminated the possibility of time spreads, we will have to look for spreads in the ratio vertical category (negative gamma, negative vega). With ten different May options (five calls and five puts), it is possible to construct a wide variety of spreads which fall into this category. How can we make an intelligent decision about which spread might be best?

我们暂时只关注 5 月的期权。既然排除了时间价差的可能性，我们就需在比率垂直价差类别中寻找合适的组合（负伽玛，负维加）。在 5 月的十种不同期权（五个看涨期权和五个看跌期权）中，可以构建出多种符合该类别的价差。那么，如何才能更明智地选择最佳价差呢？

Suppose we choose three possible strategies and try to analyze them. The three strategies which have been chosen are spreads 1, 2, and 3, shown in Figure 9-2.

假设我们选择了三种可能的策略并进行分析。这三种策略分别为价差 1、2 和 3，详见图 9-2。

These are certainly not the only possible spreads, nor can we be certain that they are the best possible spreads. But in theory each spread ought to be profitable under the given market conditions, since each fits into the ratio vertical spread category: spread 1 is a short straddle, spread 2 is a call ratio vertical spread, and spread 3 is a long put butterfly. How can we evaluate the relative merits of each spread?

这些并非唯一的可能价差组合，也无法保证它们是最佳的。但理论上每个组合在当前市场条件下应是有利可图的，因为它们都属于比率垂直价差类别：组合 1 是空跨式价差，组合 2 是看涨期权的比率垂直价差，而组合 3 是看跌期权的蝶式价差。那么，我们如何评估每个组合的相对优点呢？

Initially it may appear that spread 1 is best since it has the greatest theoretical edge. If the volatility estimate of 15% turns out to be correct, spread 1 will show a profit of 2.86, while spread 2 will show a profit of 1.00, and spread 3 will show a profit of only 40.

最初看来，组合 1 可能是最佳选择，因为它有最大的理论优势。如果 15% 的波动率估计正确，组合 1 将盈利 2.86，而组合 2 将盈利 1.00，组合 3 仅盈利 0.40。

But is theoretical edge our only concern? If that were true we could simply do each spread in bigger and bigger size to make the theoretical edge as large as we want. Instead of doing spread 2 at 10 x 15, we might increase the size fivefold to 50 x 75. This will increase the theoretical edge fivefold to 5.00, and ostensibly makes spread 2 a better strategy than spreads 1 and 3. Clearly, theoretical edge can't be the only consideration.

但理论优势是唯一的考量因素吗？若是如此，我们可以通过增加组合规模来无限提高理论优势。例如，不再将组合 2 设为 10 x 15，而是将其增加五倍至 50 x 75，从而使理论优势增加至 5.00，似乎比组合 1 和 3 更好。显然，理论优势并非唯一考虑因素。

Theoretical edge is only an indication of what we expect to earn if we are right about market conditions. Since there is no guarantee that we will be right, we must give at least as much consideration to the question of risk. If we are wrong about market conditions, how badly might we be hurt?

理论优势只是我们在市场条件正确时预期的收益指引。由于无法确保判断准确，我们必须同样重视风险问题。如果市场判断错误，可能面临多大损失？

In order to focus on the risk considerations, let's change the size of spreads 2 and 3 so that their theoretical edge is approximately equal to that of spread 1. We can achieve this by tripling the size of spread 2 to 30 x 45, and increasing the size of spread 3 sevenfold to 70 x 140 x 70. The spreads in their new sizes with their total theoretical edge and risk sensitivities are shown in Figure 9-3.

为了专注于风险考量，我们可以调整组合 2 和 3 的规模，使其理论优势接近组合 1。通过将组合 2 扩大三倍至 30 x 45，将组合 3 的规模增至 70 x 140 x 70，即可实现。图 9-3 展示了调整后的组合规模、总理论优势及风险敏感性。

With all three spreads having approximately the same theoretical edge, we can now focus on the risks associated with each spread.

在三个价差组合的理论优势大致相同的情况下，我们可以专注于各自的风险。

As with all volatility spreads, one of the risk considerations is the possibility of an incorrect volatility estimate. Since each spread has a negative vega, there will be no problem if volatility turns out to be lower than 15%. In that case, the value of each spread will increase and we will show a greater profit than originally expected. On the other hand, if volatility turns out to be greater than 15%, this could present a problem. What will happen if volatility turns out to be 17%, or 20%, or some higher number? Each spread will be hurt due to the negative vega, but each spread may not be hurt to the same degree.

对于所有波动率价差组合而言，风险之一在于波动率估计可能错误。由于每个组合的 vega 为负，如果实际波动率低于 15%，则没有问题，这样每个组合的价值都会上升，实际利润也会高于预期。然而，如果实际波动率高于 15%，可能就会出现问题。当波动率上升至 17%、20% 甚至更高时会发生什么？每个组合都会因为负 vega 受到影响，但影响程度可能各不相同。

One way to analyze the volatility risk associated with each spread is to use a theoretical pricing model to simulate the value of each spread at increasingly greater volatilities. From these values we can construct graphs reflecting each spread's theoretical edge versus volatility. Such a graph is shown in Figure 9-4.

分析每个组合的波动风险的一种方法是使用理论定价模型，模拟在不断提高的波动率下每个组合的价值。从这些数据中，我们可以绘制出每个组合的理论优势与波动率的关系图，如图 9-4 所示。

With our size adjustments each spread now has approximately the same initial theoretical edge, enabling us to focus on the volatility risk associated with each spread. Looking at Figure 9-4 we can see that each spread, 1, 2, and 3, loses its theoretical edge as volatility increases. But the slope of spread 1 is most severe. It loses its value very quickly as volatility increases, much more quickly than spreads 2 and 3.

通过调整规模，现在每个价差组合初始理论优势相当，这使我们能够集中于各自的波动率风险。查看图 9-4，可以看到随着波动率的上升，价差组合 1、2 和 3 的理论优势都在减小。但价差组合 1 的斜率最为陡峭，随波动率的上升其价值下降速度远快于组合 2 和 3。

For each of our spreads we might logically ask how high volatility can rise before we begin to lose money. That is, we might want to determine the break-even volatility, or implied volatility, for each spread. This is simply an extension of the general definition of implied volatility: the volatility which would have to occur over the life of an option, or options, such that a position would show neither a profit nor a loss. It is common among traders to determine the implied volatility of a spread position, just as they determine the implied volatility of individual options. We can see from Figure 9-3 that the implied (break-even) volatilities of spreads 1, 2, and 3 are approximately 17%, 20%, and 22%, respectively.

对于每个价差组合，我们可以合理地问波动率需要上升到多高才会开始亏损。也就是说，我们可能希望确定每个组合的盈亏平衡波动率，或隐含波动率。这是隐含波动率通用定义的延伸：在期权有效期内，如果某个波动率使组合既不盈利也不亏损，即为该组合的隐含波动率。交易者通常会计算价差组合的隐含波动率，就像计算单个期权的隐含波动率一样。从图 9-3 可以看出，组合 1、2 和 3 的隐含（盈亏平衡）波动率大约为 17%、20% 和 22%。

From a volatility perspective, spread 3 shows the best risk/reward characteristics. With each spread we are, in a sense, selling volatility, and we would like to do so at the highest possible price. Would we rather sell something that's worth 15% (our volatility estimate) at 17% (the implied volatility of spread 1), at 20% (the implied volatility of spread 2), or at 22% (the implied volatility of spread 3)? The higher the implied volatility of the spread, the greater the margin for error in our volatility estimate and, consequently, the greater the likelihood of showing a profit. Spread 1 has only a 2-percent-age-point margin for error, while spread 3 has a margin for error more than three times greater, at 7 percentage points. Spread 2 falls somewhere in between.

从波动率的角度来看，组合 3 表现出最佳的风险 / 回报特性。对于每个组合而言，我们在某种程度上都是在 “卖出波动率”，并希望以尽可能高的价格卖出。我们是愿意以 17%（组合 1 的隐含波动率）、20%（组合 2 的隐含波动率）还是 22%（组合 3 的隐含波动率）出售 15%（我们的波动率估计）的价值？价差组合的隐含波动率越高，我们的波动率估计误差容忍度越大，从而更有可能获利。组合 1 的容错率仅有 2 个百分点，而组合 3 的容错率高达 7 个百分点，约为前者的三倍。组合 2 的容错率介于两者之间。

Why are we so concerned about our volatility estimate being too low? A trader might take the view that he is just as likely to overestimate as underestimate volatility. If this happens, how will it affect the potential outcome of each spread? Suppose we decide to do spread 1 and volatility turns out to be 18%, three percentage points higher than our estimate of 15%. Looking at Figure 9-4 we can see that if this happens we will lose approximately 1.21. Suppose, however, that there is an equal chance that volatility will turn out to be 12%, three percentage points lower than our estimate. In Figure 9-5, where we have extended volatility down to 10%, we can see that in this case we will make approximately 6.95. In a more extreme case, when volatility turns out to be 20% we will lose 3.95. But if volatility turns out to be 10% we will make 9.64. For each time we underestimate volatility and show an unexpected loss, we might assume there will be an equal number of times when we overestimate volatility and show an unexpected profit. The end result of all these outcomes will be an average profit of approximately 2.86, the predicted profit of the spread at a volatility estimate of 15%.

为什么我们如此担心波动率估计过低？交易者可能认为自己同样有可能高估或低估波动率。如果这样，如何影响各组合的潜在结果？假设我们选择组合 1，而实际波动率为 18%，比 15% 的估计高出三个点。从图 9-4 可以看到，这种情况下我们会亏损约 1.21。然而，如果波动率为 12%，比估计低三个点（见图 9-5），我们将盈利约 6.95。极端情况下，当波动率达 20% 时，我们将亏损 3.95；而若波动率降至 10%，我们将盈利 9.64。每次低估波动率带来意外亏损时，我们可以假设同样次数的高估波动率会带来意外盈利。所有这些结果的平均收益约为 2.86，即波动率估计为 15% 时的预期收益。

Suppose that the average result of doing any one of our spreads, 1, 2, and 3, is a profit of approximately 2.80. If the outcome in each case is identical, why should it make any difference which spread we choose? While the end result is certainly an important theoretical consideration, how the end result comes about may be an equally important practical consideration.

假设每个组合 1、2 和 3 的平均收益约为 2.80。如果每种组合的结果相同，为什么选择哪个组合会有所不同？虽然最终收益是重要的理论考量，但获得结果的方式在实际操作中也同样关键。

Every trader knows that there are times when he shows a profit and times when he shows a loss. No one wins all the time. In the long run, however, a good trader's profits will more than offset his losses. For example, suppose a trader chooses a strategy which will show a profit of $7,000 half of the time, and which will show a loss of $5,000 the other half of the time. In the long run he will show an average profit of $1,000. But suppose the first time the trader executes the strategy he loses $5,000 and the trader only has $3,000? Now the trader will not be able to stay in business for all those times when he is fortunate enough to show a profit of $7,000. Every trader knows that it is only over long periods of time that good luck and bad luck even out. No experienced trader will initiate a strategy where short-term bad luck might terminate his trading career. This is the reason an experienced option trader will tend to avoid spread 1.

每个交易者都知道，有时盈利，有时亏损。没有人能一直赢，但长期来看，优秀的交易者会通过收益覆盖亏损。例如，假设某策略一半时间获利 7,000 美元，另一半时间亏损 5,000 美元，长期来看平均盈利 1,000 美元。但如果交易者第一次执行策略时亏损 5,000 美元，而手头仅有 3,000 美元呢？这样交易者将无法继续参与市场，错过未来获利 7,000 美元的机会。每位交易者都知道，只有长期操作，幸运与不幸才会均衡。没有经验的交易者会冒短期运气不佳导致交易生涯终结的风险。正因如此，有经验的期权交易者往往会避免选择组合 1。

Any financial officer knows that it is much easier to manage a steady cash flow rather than one that swings wildly. This is equally true for an option trader. He must sensibly manage his finances so that he can avoid being ruined by the periods of bad luck which will inevitably occur, no matter how skillfully he trades.

任何财务官员都明白，管理稳定的现金流要比管理剧烈波动的现金流容易得多。对期权交易者而言同样如此。他必须合理管理资金，以避免因不可避免的运气不佳而导致破产，无论交易技巧多么娴熟。

An incorrect volatility estimate may not be the only risk with which an option trader must be concerned. Every input into a theoretical pricing model represents a risk to the trader since an incorrect input may alter an option's theoretical value. These risks are reflected in the delta, gamma, theta, vega, and rho associated with a spread. We can summarize these risks as follows:

波动率估计错误并非期权交易者唯一的风险。理论定价模型中的每个输入都是潜在风险，因为错误的输入会改变期权的理论价值。这些风险反映在组合的 delta、gamma、theta、vega 和 rho 上。我们可以将这些风险总结如下：

Delta (Directional) Risk-The risk that the underlying market will move in one direction rather than another. When we create a position which is delta neutral, we are trying to ensure that initially the position has no particular preference as to the direction in which the underlying instrument will move. A delta neutral position does not necessarily eliminate all directional risk, but it usually leaves us immune to directional risks within a limited range.

Delta（方向性）风险 - 标的市场朝某一特定方向移动的风险。当我们创建一个 delta 中性的头寸时，我们希望确保该头寸对标的产品的移动方向没有特别偏好。delta 中性头寸并不完全消除方向性风险，但通常可以让我们在有限范围内免受方向性风险的影响。

Gamma (Curvature) Risk-The risk of a large move in the underlying contract, regardless of direction. The gamma position is a measure of how sensitive a position is to such large moves. A positive gamma position does not really have gamma risk since such a position will, in theory, increase in value with movement in the underlying contract. A negative gamma position, however, can quickly lose its theoretical edge with a large move in the underlying contract. The consequences of such a move must always be a consideration when analyzing the relative merits of different positions.

Gamma（曲率）风险 - 标的合约大幅波动的风险，不论方向。gamma 反映了头寸对这种大幅波动的敏感性。正 gamma 头寸理论上不会有 gamma 风险，因为它会随着标的合约的波动增值；但负 gamma 头寸可能会因标的合约的大幅波动迅速丧失其理论优势。因此，在分析不同头寸的相对优势时，始终需要考虑这种波动的后果。

Theta (Time Decay) Risk-The risk that time will pass with no movement in the underlying contract. This is the opposite side of gamma risk. Positions with positive gamma become more valuable with large moves in the underlying. But if movement helps, the passage of time hurts. A positive gamma always goes hand in hand with a negative theta. A trader with a negative theta will always have to consider the risk in terms of how much time can pass before the spread's theoretical edge disappears. The position wants movement, but if the movement fails to occur within the next day, or next week, or next month, will the spread, in theory, still be profitable?

Theta（时间衰减）风险 - 随着时间推移标的合约没有波动的风险。这与 gamma 风险相对。正 gamma 头寸会因标的合约的大幅波动而增值，但如果波动有利，则时间的推移就不利。正 gamma 通常伴随着负 theta。拥有负 theta 的交易者必须考虑时间在消耗头寸的理论优势方面的风险。该头寸需要波动，但如果未来一天、一周甚至一个月内都未发生波动，理论上头寸还能盈利吗？

Vega (Volatility) Risk-The risk that the volatility which we input into the theoretical pricing model will be incorrect. If we input an incorrect volatility, we will be assuming an incorrect distribution of underlying prices over time. Since some positions have a positive vega and are hurt by declining volatility, and some positions have a negative vega and are hurt by rising volatility, the vega represents a risk to every position. A trader must always consider how much the volatility can move against him before the potential profit from a position disappears.

Vega（波动率）风险 - 输入理论定价模型的波动率可能不准确的风险。输入不准确的波动率会导致对标的价格分布的错误假设。某些头寸拥有正 vega，因波动率下降而受损；另一些头寸拥有负 vega，因波动率上升而受损。因此 vega 是每个头寸的风险。交易者必须考虑波动率变动的程度对利润的影响。

Rho (Interest Rate) Risk—The risk that interest rates will change over the life of the option. A position with a positive rho will be helped (hurt) by an increase (decline) in interest rates, while a position with a negative tho will show just the opposite characteristics. (footnote 1: Of course, we are only considering the Interest rate risk as It applies to the evaluation of options. Changes in interest rates can also affect the evaluation of an underlying contract, such as a bond, or even the shares in a company. But that is a separate matter.) Generally, the interest rate is the least important of the inputs into a theoretical pricing model, and it is unlikely, except for special situations, that a trader will give extensive thought to the rho risk associated with a position.

Rho（利率）风险 - 在期权存续期间利率变化的风险。正 rho 的头寸会因利率上升（下降）而获利（受损），负 rho 头寸则相反。（脚注 1：这里只考虑利率风险对期权评估的影响，利率变化也会影响标的合约的估值，如债券或公司股票，但这是另一问题。）通常利率是理论定价模型中最不重要的输入，除非特殊情况，交易者一般不会过多考虑头寸的 rho 风险。

So far we have compared only the volatility risk associated with spreads 1, 2, and 3. Is there any other risk with which we ought to be concerned? All of our spreads have a negative gamma, so they will all be adversely affected by a large move in the underlying contract. In order to compare the relative gamma risks, we can construct a graph showing the values of the spreads at varying prices of the underlying contract. This has been done in Figure 9-6. Again, we assume that each spread has approximately the same theoretical value under our theoretical assumptions, in this case at the current underlying price of 49.50.

到目前为止，我们只比较了组合 1、2 和 3 的波动率风险。那么是否还有其他需要关注的风险？所有组合都具有负 gamma，因此它们都将受到标的合约大幅波动的不利影响。为了比较各组合的 gamma 风险，我们可以绘制一张图，显示标的合约价格不同情况下组合的价值变化。这在图 9-6 中已经展示出来。同样假设在理论条件下，各组合在当前标的价格 49.50 时的理论价值相当。

Looking at Figure 9-6 we can see that if the underlying contract makes a large upward move, spread 3 will be the least affected. It can stand a move up to 52.75 without losing its positive theoretical edge. Spreads 1 and 2 can stand upward moves to only 51.05 and 51.75, respectively. On the downside, spread 1 is still the riskiest since it loses all its theoretical edge if the underlying market should make a swift move down to 47.90. Spread 3 is less risky because it can stand a move down to 47.50. But the least risky on the downside is clearly spread 2, since it never loses all its theoretical edge. In the most extreme downward move the theoretical edge of spread 2 will collapse to approximately zero.

从图 9-6 可以看出，如果标的合约大幅上涨，组合 3 受影响最小，它能承受价格涨至 52.75 而不失去其正理论优势。而组合 1 和 2 分别只能承受上涨至 51.05 和 51.75 的波动。在价格下跌方面，组合 1 依然风险最高，一旦标的市场快速下跌至 47.90 便会失去全部理论优势。组合 3 风险较小，可承受价格跌至 47.50。风险最低的是组合 2，即便在极端的下跌情况下其理论优势也仅会降至接近零。

PRACTICAL CONSIDERATIONS
实际考量

Considering the vega and gamma risk, spread 3 seems to have the best risk characteristics. It has a larger margin for error in terms of volatility than either spread 1 or 2. In terms of underlying price movement it can also stand a larger upward move than the other two spreads. Only when we consider the possibility of a large downward move does spread 3 not display the best risk characteristics. In this case spread 2 comes in first. But spread 3 still looks better than spread 1. In theory, a trader ought to be more willing to execute spread 3 than either spread 1 or 2. In the real world, however, practical trading considerations may play a role in the trader's decision.

综合 vega 和 gamma 风险来看，组合 3 的风险特性似乎最好。它的波动率容错空间比组合 1 或 2 大。在标的价格的波动方面，它也能承受比另外两个组合更大的上行波动。只有在考虑大幅下跌的情况下，组合 3 的风险特性才不及其他组合，此时组合 2 表现最佳，但组合 3 仍优于组合 1。从理论上讲，交易者更应该倾向于执行组合 3。然而在实际交易中，一些实际因素可能会影响决策。

Even though spread 3, the butterfly, appears to be the best theoretical choice of the three, it has some practical drawbacks which may make it an unrealistic choice. Spread 3 is a three-sided spread, as opposed to spreads 1 and 2, which are two-sided. A three-sided spread will probably be more difficult to execute in the marketplace, and is likely to cost more in terms of the total width of the bid/ ask. If a trader wants to execute the complete spread at one time, as is most common, he may not be able to do so at his target prices. If, on the other hand, he tries to execute one leg (footnote 2: The options which comprise a spread position are sometimes referred to as the legs of the spread.) at a time, he will be at risk from adverse changes in the market until the other legs have been executed.

尽管组合 3（蝶式价差）在理论上最优，但它在操作上存在一些难点，使其不太现实。组合 3 是一个三边组合，而组合 1 和 2 则是双边组合。三边组合在市场中可能更难成交，且可能导致更高的买卖差价成本。如果交易者希望一次性完成整个组合（这种方式最常见），可能无法按预期价格成交；如果逐一执行各个部分（脚）（脚注 2：脚是指构成价差组合的各个期权部分），则在其他部分成交前会面临市场变动的风险。

Additionally, there is the question of market liquidity. In order to obtain a theoretical edge commensurate with spreads 1 and 2, it was necessary to increase the size of the butterfly sevenfold to 70 x 140 x 70. If there is insufficient liquidity in the May 49, 50, and 51 puts to support this size, it may not be possible to execute the butterfly in the size required to meet our profit expectations. Alternatively, we may be able to execute part of the spread at favorable prices, but as we increase the size, the prices may become less satisfactory. Moreover, for a retail customer the increased size may entail significantly greater transaction costs.

此外，市场流动性也是一个问题。为了获得与组合 1 和 2 相当的理论优势，必须将蝶式组合的规模增加到 70 x 140 x 70。如果 5 月 49、50 和 51 看跌期权的流动性不足以支持这一规模，那么可能无法按照预期的规模完成交易，无法实现预期利润。或者，虽然能在有利价格下完成部分组合，但随着规模的增加，价格可能变得不理想。此外，对于散户来说，增加规模可能会显著增加交易成本。

If trading considerations make spread 3 impractical, we may have to choose between spreads 1 (the straddle) and 2 (the ratio vertical spread). If that happens, spread 2 is the clear winner. It allows for a much greater margin for error in both volatility (vega risk) and underlying price change (gamma risk). A trader who is given a choice between these two spreads will strongly prefer spread 2.

如果实际交易考虑使得组合 3 不切实际，我们可能需要在组合 1（跨式）和组合 2（比率垂直价差）之间做选择。在这种情况下，组合 2 显然是更好的选择。它在波动率（vega 风险）和标的价格变动（gamma 风险）方面提供了更大的容错空间。如果只能在这两种组合中选择，交易者会明显倾向于组合 2。

The choice of spreads may not always be as clear as in this example. The superiority of spread 3, at least from the theoretical standpoint, was relatively obvious. Sometimes, however, one spread may be superior with respect to one type of risk, while a different spread may be superior with respect to a different risk.

不过，组合的优劣并非总是像这个例子那样明显。组合 3 在理论上优越性较为显著，但有时，一种组合在某一风险类型上表现优越，而另一种组合则在不同风险上更胜一筹。

Let's consider three new spreads, 4 (a ratio vertical spread), 5 (a short time spread), and 6 (a diagonal spread). The total theoretical edge of each spread, as well as their risk sensitivities (all taken from the theoretical evaluation table in Figure 9-1), are shown in Figure 9-7. In order to again focus on the risks associated with each spread, the size of each spread has been adjusted to yield approximately the same theoretical edge.

我们来看看三个新的组合，组合 4（比率垂直价差）、组合 5（短期时间价差）和组合 6（对角价差）。每个组合的理论总收益以及风险敏感性（均来自图 9-1 的理论评估表）列在图 9-7 中。为了集中比较各组合的风险，每个组合的规模都已调整至大致相同的理论收益。

Since each spread has a negative vega, we will want to consider the volatility risk if volatility should turn out to be greater than our estimate of 15%. The sensitivity of each spread to increasing volatility is shown in Figure 9-8. We can see that spread 4 has an implied volatility of approximately 18.1%, spread 5 approximately 17.0%, and spread 6 approximately 17.2%. If an increase in volatility is our primary concern, then spread 4 (the ratio vertical spread) seems to offer the best risk characteristics.

由于每个组合都具有负 vega，我们需要考虑波动率风险，如果波动率超过预估的 15%。图 9-8 展示了每个组合对波动率上升的敏感性。可以看出，组合 4 的隐含波动率约为 18.1%，组合 5 约为 17.0%，组合 6 约为 17.2%。如果主要关注波动率上升的风险，组合 4（比率垂直价差）似乎提供了最好的风险特性。

In addition to the volatility risk, we can see that spread 4 also has a negative gamma, so that it will be adversely affected by a sudden large move in the underlying contract. If we are concerned about the possibility of such a move we may want to determine exactly how a large move in the price of the underlying contract will affect the value of the spread. Figure 9-9 shows the sensitivity of each of our spreads, 4, 5, and 6, to a change in the price of the underlying contract. (footnote 3: We assume here that the May and July underlying contracts maintain the same approximate relationship. That is, the July contract is always 1.0123 times the May contract since 50.11/49.50 = 1.0123. The x-axis in Figure 9-9 is the price of the May contract.)

除了波动率风险外，我们也注意到组合 4 具有负 gamma，这意味着标的资产的突然大幅波动会对其不利。如果对这种大幅波动存在担忧，可以进一步分析标的价格变动对组合价值的影响。图 9-9 展示了组合 4、5 和 6 对标的价格变动的敏感性。（脚注 3：假设 5 月和 7 月的标的合约大致保持相同的比例关系，即 7 月合约始终为 5 月合约的 1.0123 倍，因为 50.11/49.50=1.0123。图 9-9 的 x 轴表示 5 月合约的价格。）

Note that spread 4 has the narrowest profit range of the three spreads, in theory losing all its theoretical value if the market should immediately drop below 46.50 or rise above 52.20. On the other hand, spread 6 has very little downside risk and can still stand an immediate move upward to about 52.30. If a trader were worried about the possibility of a swift fall in the market, he might be willing to give up the extra volatility cushion offered by spread 4 over spread 6 (18.0% vs. 17.2% for the additional downside protection offered by the latter spread. This is reflected in the smaller negative gamma associated with spread 6 as compared with spread 4.

注意到组合 4 的理论收益范围最窄，如果市场迅速跌至 46.50 以下或升至 52.20 以上，组合 4 的理论价值将全部损失。而组合 6 的下行风险很小，即便市场迅速升至约 52.30，它仍能承受。如果交易者担心市场快速下跌，他可能会愿意放弃组合 4 相比组合 6 提供的额外波动率缓冲（18.0% 对比 17.2%）以获得后者的下行保护。这也反映在组合 6 的负 gamma 小于组合 4。

Finally, we can see that spread 5, while having the least desirable volatility risk, also has a positive gamma. This means that any large move in the underlying contract will increase the value of the position. If a trader were worried about the possibility of a sudden large move in the underlying contract, but were not overly concerned with an increase in volatility, he might be willing to accept the less desirable volatility risK associated with spread 5 for the more desirable positive gamma characteristics.

最后，我们可以看到，虽然组合 5 的波动率风险最不理想，但它拥有正 gamma。这意味着标的资产的任何大幅波动都会增加该头寸的价值。如果交易者担心标的资产可能出现突发大幅波动，但对波动率上升的担忧不大，他可能会愿意接受组合 5 的较差波动率风险，以获得正 gamma 带来的优势。

A trader who executes spread 5 will have a positive gamma, so he has no gamma risk. But he will have a theta risk if the underlying contract fails to move. How great is the risk? Figure 9-10 shows the sensitivity of all three spreads to the passage of time. Since spreads 4 and 6 have negative gammas, they can only gain value with the passage of time. On the other hand, spread 5 loses value as each day passes. Looking at the graph associated with this spread, we can see that if no movement occurs in the underlying contract, the spread loses all its theoretical edge after about 18 days. This is the price one has to pay for the privilege of having a positive gamma.

执行组合 5 的交易者将拥有正 gamma，因此不存在 gamma 风险，但如果标的资产不动，他会面临 theta 风险。风险有多大？图 9-10 展示了三种组合随时间推移的敏感性。由于组合 4 和 6 具有负 gamma，时间的流逝只会增加它们的价值。而组合 5 则会随着每一天的过去而损失价值。从该组合的图表中可以看出，如果标的资产没有波动，约 18 天后组合的理论优势将完全消失。这就是拥有正 gamma 的代价。

If one has to choose from among spreads 4, 5, or 6, which spread is best? The situation is not clear-cut, and the answer will probably depend on a trader's experience in the market. If he feels that an increase in implied volatility represents the greatest risk, he will probably choose spread 4. If he feels that a large move in the underlying contract represents the greatest risk, he will probably choose spread 5. And if he is willing to settle for partial protection against both volatility and market movement, he will probably choose spread 6.

如果必须在组合 4、5 或 6 中选择，哪个组合最佳？答案并不明确，这可能取决于交易者的市场经验。如果他认为隐含波动率增加是最大风险，他可能会选择组合 4；如果认为标的资产的大幅波动是最大风险，则可能会选择组合 5；而如果他希望同时获得部分波动率和市场波动的保护，那么组合 6 可能会是他的选择。

As must by now be obvious, the choice of spreads is never a simple matter of right and wrong. Like all trading decisions, it is a question of risk and reward. While there are many risks with which an option trader must deal, he will often have to ask himself which risk represents the greatest threat. Sometimes, in order avoid one type of risk, he will be forced to accept a different risk. Even if the trader is willing to accept some risk in a certain area, he may decide that he will only do so to a limited degree. Then he may have to accept increased risks in other areas.

显然，选择期权组合从来不是对错的问题，而是权衡风险和回报。期权交易者面临诸多风险，往往要思考哪个风险对自己威胁最大。有时，为了规避某类风险，可能不得不接受另一种风险。即使愿意在某些方面承担风险，交易者也可能仅愿意在一定限度内承担，这可能会导致在其他方面面临更大的风险。

If given the choice between several different spreads a trader can use a computer, as was done in the foregoing examples, to study the risk characteristics of the different spreads. Unfortunately, it may not always be possible to analyze the choices in such detail, A trader may not have the necessary computer support at his disposal, or market conditions may be changing so rapidly that if he fails to make an immediate decision opportunity may quickly pass him by. Is there any way to make a quick comparison of spreads without doing a detailed graphic analysis?

当面对多种组合选择时，交易者可以使用计算机（如前例所示）来研究不同组合的风险特性。但并非总能如此详细地分析，有时交易者可能缺乏必要的计算机支持，或市场变化过快，若未能及时决策，机会就可能稍纵即逝。那么，有没有快速比较组合的方法，而无需进行详细的图形分析？

One method that traders sometimes use is to think of every spread as a tradeoff between risk and reward. We might express this tradeoff as a fraction, risk/reward. If a trader goes into the marketplace, he would like to have the greatest possible reward. At the same time he would like to have the least possible risk. Indeed, the ideal risk/reward fraction would be 0 + ∞o (zero risk, infinite reward). But 0 + ∞ = 0, so that if we express the risk/reward characteristics of each spread as a fraction, risk/ reward, then in theory the spread whose fraction is closest to zero has the best tradeoff between risk and reward.

交易者有时会将每个组合视为风险与回报之间的权衡，可以用 “风险 / 回报” 比来表达这种权衡。当进入市场时，交易者希望获得最大回报，同时尽量降低风险。理想的风险 / 回报比应为 “0 + ∞”（零风险、无限回报）。但由于 0 + ∞ = 0，因此在理论上，风险 / 回报比越接近零的组合，风险与回报的权衡就越好。

What numbers should we use to express the risk and reward for a spread? The reward is what we expect to make when we are right about market conditions. This is simply the theoretical edge, and we can therefore make the theoretical edge the denominator of our fraction. What about the numerator, or risk component? Here we may have to deal with several different numbers since option positions are subject to many different risks. These risks are represented by the various option sensitivities. The practical approach is to express the numerator of our fraction with the sensitivity with which we are most concerned. For example, if a change in volatility is our greatest concern, we can use the vega of the spread as our numerator. If choosing from among several different spreads, the spread whose vega/theoretical edge is closest to zero will have the most desirable risk/reward characteristics. In the same way, if a large price move is our greatest concern, the spread whose gamma/theoretical edge is closest to zero will have the most desirable risk/ reward characteristics.

应该使用哪些数字来表示组合的风险和回报？回报是我们在对市场情况判断正确时的预期收益，即理论优势，所以理论优势可以作为分母。那么分子或风险部分如何表达？由于期权头寸面临多种风险，可以用与具体风险相关的灵敏度来表达分子。比如，如果最担心波动率变化，可以用组合的 Vega 作为分子。比较多个组合时，Vega/ 理论优势最接近零的组合具有最优的风险 / 回报特性。同样地，如果最担心价格大幅波动，则 Gamma/ 理论优势最接近零的组合风险 / 回报特性最好。

Let's try to analyze spreads 4, 5, and 6 using this method. One risk with which we will certainly have to be concerned is the possibility of a change in volatility. Calculating the vega/theoretical edge, we have:

Spread 4:	-.840/2.70	=	-311
Spread 5:	-1.850/3.00	=	-.617
Spread 6:	-1.340/2.90	=	-462

From the above calculations we can see that spread 4 has the best volatility characteristics since its vega/theoretical edge is closest to zero. This is the same conclusion we reached from Figure 9-8, but without the necessity of doing a detailed study of each spread.

我们尝试用此方法分析组合 4、5 和 6。波动率变化是我们关注的风险之一。计算 Vega/ 理论优势得到：

价差 4：	-.840/2.70	=	-311
价差 5：	-1.850/3.00	=	-.617
价差 6：	-1.340/2.90	=	-462

从以上计算可以看出，组合 4 的 Vega/ 理论优势最接近零，因此波动率特性最佳。这与图 9-8 的结论一致，但无需对每个组合做详细研究。

Note that when we divide the sensitivity of a spread by its theoretical value, the result is independent of the size of the spread. If we had done spread 4 twice as large (40 x 60 instead of 20 x 30) this would have doubled the size of both the vega and the theoretical edge. The resulting fraction would still have been -311.

注意，当我们用组合的灵敏度除以其理论价值时，结果与组合规模无关。若将组合 4 的规模翻倍（从 20x30 增加到 40x60），Vega 和理论优势也会翻倍，但结果仍为-0.311。

What about the risk of a large move in the price of the underlying contract? We do not need to worry about large price moves in spread 5 since its positive gamma means that a large move can only enhance the value of the position. However, we might still want to compare spreads 4 and 6 for gamma risk. Dividing the gamma by the theoretical edge we have:

Spread 4:	-.72.0/2.70	=	-26.7
Spread 6:	-56.0/2.90	=	-19.3

We can see that spread 6 is at less risk from a large move in the price of the underlying contract because -19.3 is closer to zero than -26.7. This confirms the conclusion from Figure 9-9.

再来看标的资产价格大幅波动的风险。由于组合 5 的 Gamma 为正，价格大幅波动只会增加其价值，不用担心。但我们仍然可以对组合 4 和 6 的 Gamma 风险进行比较。计算 Gamma/ 理论优势得到：

价差 4：	-72.0/2.70	=	-26.7
价差 6：	-56.0/2.90	=	-19.3

可以看出，组合 6 对价格大幅波动的风险较低，因为-19.3 更接近零，验证了图 9-9 的结论。

A word of warning about this method of estimating the relative riskiness of a spread. Because an option's sensitivities are only well defined within a narrow range, dividing the risk sensitivity by the theoretical edge offers only an estimate of the relative riskiness of a position. Consider, for example, the relative volatility risks of spreads 1, 2, and 3. Dividing the vega by the theoretical value for each spread we have:

Spread 1:	-1.368/2.86	=	-.478
Spread 2:	-435/3.00	=	-145
Spread 3:	-.630/2.80	=	-.225

From these numbers it appears that spread 2 is the least risky with respect to volatility since -. 145 is closer to zero than - 478 or -225. But going back to Figure 9-4 we find that spread 3 actually has the highest implied volatility, and therefore the least volatility risk. Even so, this method would have at least warned us away from spread 1, which clearly has the greatest volatility risk.

需要提醒的是，此方法只能估算组合的相对风险。由于期权灵敏度仅在狭窄范围内定义，用风险灵敏度除以理论优势只能大致估算组合的风险。例如，组合 1、2 和 3 的相对波动率风险。将 Vega 除以理论价值得到：

价差 1：	-1.368/2.86	=	-.478
价差 2：	-435/3.00	=	-145
价差 3：	-.630/2.80	=	-.225

从数字来看，组合 2 在波动率方面风险最小，因为-0.145 更接近零。但回到图 9-4 我们发现，组合 3 的隐含波动率最高，因此波动率风险最小。尽管如此，该方法至少提示我们远离组合 1，因为它的波动率风险显然最大。

Sometimes, if a trader is under great pressure to make a quick decision, he may not have the time to make even a cursory analysis of relative riskiness of various spreads. In such cases, he will often have to rely on his instincts in choosing a strategy. While there is no substitute for experience, most traders quickly learn an important rule: stradales and strangles are the riskiest of all spreads. This is true whether one buys or sells these strategies. New traders sometimes assume that the purchase of straddles and strangles is not especially risky because such strategies have limited risk. But it can be just as painful to lose money day after day when one buys a straddle or strangle and the market fails to move, as it is to lose the same amount of money all at once when one sells a straddle and the market makes a violent move. Of course, a trader who is right about volatility can reap large rewards from straddles and strangles. But an experienced trader knows that such strategies offer the least margin for error, and he will usually prefer other strategies with more desirable risk characteristics.

有时交易者在压力下需迅速做出决策，甚至没有时间对各种组合的相对风险性进行简单分析。这种情况下，往往只能凭直觉选择策略。尽管经验无可替代，但大多数交易者都会迅速领悟一个重要原则：跨式和宽跨式价差是所有价差中风险最大的组合。不论买入或卖出这些策略，风险都不小。新手有时认为购买跨式和宽跨式不算特别冒险，因为这些策略的风险有限。但在买入跨式或宽跨式后，如果市场未如预期波动，每天都在亏损，这种持续损失的痛苦并不亚于卖出跨式时市场剧烈波动带来的瞬间亏损。当然，若对波动性判断准确，跨式和宽跨式可以带来丰厚回报。但有经验的交易者知道这些策略的容错空间最小，通常会选择风险特性更为理想的策略。

HOW MUCH MARGIN FOR ERROR?
允许多大误差？

New traders sometimes ask what is a reasonable margin for error in assessing the inputs into a theoretical pricing model, particularly when it comes to the volatility input. As is often the case, it will depend on the trader's experience in the market in which he is trading. In some cases, 5 percentage points may be an extremely large margin for error, and the trader will feel very confident with any strategy passing such a test. In other cases, five percentage points may be almost no margin for error at all, and the trader will find that the strategy is a constant source of worry.

新手有时会问，在评估理论定价模型的输入时（特别是波动性输入），合理的误差范围是多少。通常，这取决于交易者在市场中的经验。在某些情况下，5 个百分点的误差范围可能非常宽泛，交易者会对任何通过该测试的策略充满信心；而在另一些情况下，5 个百分点几乎没有容错空间，交易者可能会因策略而时常担忧。

Perhaps a better way to approach the question is to ask not what is a reasonable margin for error, but rather to ask what is the correct size in which to do a spread given a known margin for error. Practical trading considerations aside, a trader should always choose the spread with the best risk/reward characteristics. But sometimes even the best spread will have only a small margin for error, and consequently entail significant risk. In such cases a trader, if he wants to make a trade, ought to do so in small size. If, however, a trader can execute a spread with a very large margin for error, he ought to be willing to do the spread in much larger size.

或许更好的思路不是问合理的误差范围是多少，而是问在已知的误差范围内应如何确定组合的适当规模。撇开实际交易的考虑，交易者应始终选择风险 / 收益特性最佳的组合。但有时即便是最优的组合，其误差范围也很小，因而风险较大。此时，若想交易，建议交易者缩小规模。而如果可以进行容错范围较大的组合，交易者则应愿意放大规模操作。

As an example, consider a trader whose best estimate of volatility in a certain market is 15%. If implied volatility is higher than 15% he will look for positions with a negative vega. If the best negative vega strategy the trader can find is a 1 x 2 ratio vertical spread with an implied volatility of 16/2% (only a 1/2-percentage-point margin for error), he will almost certainly keep the size of his strategy small, perhaps executing the spread only five times (5 x 10). If, however, the same spread has an implied volatility of 25% (a 10-percentage-point margin for error), and the trader has never seen volatility go that high, he may have the confidence to execute the spread in much larger size, perhaps 50 × 100. (footnote 4: Size, of course, is relative. To a well capitalized, experlenced trader even 50 x 100 may be a small trade.) The size of a trader's positions should depend on the riskiness of the positions, and this in turn depends on how much can go wrong without the strategy turning against the trader.

举个例子，假设某交易者估计某市场的波动率为 15%。如果隐含波动率高于 15%，他会寻找负 vega 的头寸。如果他找到的最佳负 vega 策略是一个 1x2 的比例垂直价差，隐含波动率为 16.2%（只有 0.5 个百分点的误差空间），他几乎肯定会将策略规模控制得较小，可能只执行五次（5x10）。但如果同一组合的隐含波动率为 25%（有 10 个百分点的误差空间），且交易者从未见过如此高的波动率，他可能会有信心将规模扩大，执行至 50×100。（脚注 4：当然，规模是相对的，对资金充足、经验丰富的交易者来说，甚至 50×100 也可能是小交易。）交易规模应取决于头寸的风险性，而风险性则取决于策略的容错空间。

DIVIDENDS AND INTEREST
红利与利息

In addition to the delta, gamma, theta, and vega risks which all traders must consider, stock option traders might also have to consider the risk of changes in dividends and interest rates. (footnote 5: Futures options can also be affected by changes in interest rates since a change in interest rates will affect the forward price of the underlying futures contract. Unlike stocks, factors other than interest rates, such as short term supply and demand, can also affect these contracts.) This is especially true of time spreads, since options with different expirations react differently to changes in these inputs.

除了所有交易者必须考虑的 delta、gamma、theta 和 vega 风险外，股票期权交易者还需考虑红利和利率变化的风险。（脚注 5：期货期权也可能受利率变化影响，因为利率变化会影响期货合约的远期价格。与股票不同，除利率外，短期供需等其他因素也会影响这些合约。）这种风险在时间价差中尤为显著，因为不同到期时间的期权对这些因素的反应不同。

Consider the evaluation table for stock options shown in Figure 9-11. With implied volatilities well below the forecast of 27%, it makes sense to look for spreads with positive vegas. Suppose we focus on four possible spreads shown in Figure 9-12. Spreads 7 and 8 are long time spreads, while spreads 9 and 10 are diagonal spreads. What are the relative merits of each spread?

请参阅图 9-11 中的股票期权估值表。当隐含波动率明显低于 27% 的预测时，寻找正 vega 的价差是合理的。假设我们关注图 9-12 中的四种可能价差。价差 7 和 8 为多头时间价差，而价差 9 和 10 为对角价差。那么，每种价差的相对优势是什么呢？

As with all option spreads, we have to consider a variety of risks. Note that in the evaluation table in Figure 9-11 we used an interest rate of 8%. Suppose we believe that interest rates are likely to rise sharply in the near future. How might these spreads react to rising interest rates? We can see from Figure 9-13 that spreads 7 and 9 will be hurt by rising interest rates, while spreads 8 and 10 will be helped. If a rise in interest rates is our primary concern, we might focus on spreads 8 and 10, regardless of any desirable vega or gamma characteristics associated with spreads 7 and 9.

与所有期权价差一样，我们必须考虑各种风险。请注意，图 9-11 的估值表中使用的利率为 8%。假设我们认为利率在不久的将来可能会大幅上升。那么这些价差对利率上升会有什么反应？从图 9-13 可以看出，价差 7 和 9 会受到利率上升的影响，而价差 8 和 10 会受益于利率上升。如果利率上升是我们主要关心的因素，那么我们可能会优先考虑价差 8 和 10，而忽略价差 7 和 9 的 vega 或 gamma 特性。

If we focus on spreads 8 and 10, we will still want to consider the volatility risk. We can do a cursory comparison of this risk by dividing the vega by the theoretical edge. From this we find:

Spread 8:	1.380/6.45	=	.214
Spread 10:	2.774/6.14	=	.452

如果我们重点考虑价差 8 和 10，仍需考虑波动率风险。我们可以通过将 vega 除以理论价值来快速对比此风险，结果如下：

价差 8：	1.380/6.45	=	.214
价差 10：	2.774/6.14	=	.452

If volatility risk is our second concern, then spread 8 is probably best because its vega divided by theoretical edge is much smaller than that of spread 10. Suppose, however, that we are more concerned with a large move in the underlying stock than with a decline in volatility. Now we can see that spread 10 is best because its positive gamma means that a large move in the price of the underlying stock can only work to our advantage. As always, the choice of strategies will require us to make some judgements as to what risks we are willing to accept, and to what degree.

如果波动率风险是我们次要的考量，价差 8 可能是最佳选择，因为其 vega 与理论价值的比值远小于价差 10。但是，如果我们更关注的是标的股票的大幅波动而非波动率下降，那么价差 10 会更合适，因为其正 gamma 意味着标的股票的价格大幅变动对我们有利。最终，选择策略时仍需权衡接受风险的种类及程度。

Finally, let's look at our spreads with respect to a change in dividends. In our evaluation table we assumed a quarterly dividend of 1.25. Suppose we believe that the dividend is likely to be increased. How will this affect our four spreads? From Figure 9-14 we can see that now spreads 7 and 9 look the best since they are helped by an increase in the dividend.

最后，来看一下红利变动对价差的影响。在估值表中，我们假设季度分红为 1.25。假设我们预计分红会增加，这对四种价差的影响如何？从图 9-14 可以看出，价差 7 和 9 在红利增加的情况下表现最佳。

What about volatility and curvature risk? Estimating the relative risks by dividing the sensitivity by theoretical edge, we have:

	Vega Risk	Gamma Risk
Spread 7:	2.275/6.75 = .337	-32.5/6.75 = -4.8
Spread 9:	1.985/6.50 = .305	-3.5/6.50 = -5

那么波动率和曲率风险呢？通过将敏感性除以理论价值来估算相对风险，我们得到：

	维加风险	伽马风险
价差 7：	2.275/6.75 = .337	-32.5/6.75 = -4.8
价差 9：	1.985/6.50 = .305	-3.5/6.50 = -5

Since there is not much difference in the spreads in terms of vega risk, we might choose spread 9 since it has much less gamma risk. At the same time, If we believe an increase in the dividend is very likely, we may prefer spread 7, since we can see from Figure 9-14 that if the dividend is increased, spread 7 shows the greatest increase in value.

鉴于两种价差的 vega 风险相差不大，我们可以选择 gamma 风险更低的价差 9。同时，如果我们认为股息增加的可能性很大，那么可以优先选择价差 7，因为从图 9-14 可见，股息增加会使价差 7 的价值提升更明显。

WHAT IS A GOOD SPREAD?
什么是好的价差？

Option traders, being human, would rather talk about their successes than their disasters. If one were to eavesdrop on conversations among traders, it would probably seem that no one ever made a losing trade. Disasters, when they do occur, only happen to other traders. The fact is every successful option trader has had his share of disasters. What separates the successful trader from the unsuccessful one is the ability to survive such occurrences.

期权交易员，毕竟是人，总是更愿意谈论自己的成功，而非失败。如果你偷听交易员们的对话，可能会觉得没有人做过亏损的交易。其实，每个成功的期权交易员都经历过一些失败。成功与否的区别在于他们能否从这些挫折中生存下来。

Consider the trader who initiates a spread with a good theoretical edge and a large margin for error in almost every risk category. If the trader still ends up losing money on the spread, does this mean that the trader has made a poor choice of spreads? Maybe a similar spread, but one with less margin for error, would have resulted in an even greater loss, perhaps a loss from which the trader could not recover.

假设一位交易员建立了一个具备良好理论优势且在大多数风险类别中有足够容错的价差。如果最终仍亏损，这是否意味着该交易员选择了一个不好的价差？也许，容错更小的类似价差会导致更大的损失，甚至让交易员难以恢复。

It is impossible to take into consideration every possible risk. A spread which passed every risk test would probably have so little theoretical edge that it wouldn't be worth doing. But the trader who allows himself a reasonable margin for error will find that even his losses will not lead to financial ruin. A good spread is not necessarily the one that shows the greatest profit when things go well; it may be the one which shows the least loss when things go badly. Winning trades always take care of themselves. Losing trades, which don't give back all the profits from the winning ones, are just as important.

不可能考虑到所有潜在风险。一个通过所有风险测试的价差，其理论优势可能小到不足以执行。但给自己留出合理的容错空间的交易员，即便亏损也不会导致财务崩溃。好的价差并不一定是在一切顺利时获利最多的，而可能是当市场不利时损失最小的。盈利交易自然会照顾好自己，而那些不会蚕食所有盈利的亏损交易同样重要。

ADJUSTMENTS
调整

In the last chapter we considered the question of when a trader should adjust a position to remain delta neutral. The trader must also consider how best to adjust, for there are many different ways to adjust the total delta position. An adjustment to a trader's delta position may reduce his directional risk, but if he simultaneously increases his gamma, theta, or vega risk, he may inadvertently be exchanging one type of risk for another.

在上一章中，我们讨论了交易员何时应调整头寸以保持 delta 中性。交易员还必须考虑如何最佳地进行调整，因为有许多方法可以调整总 delta 头寸。虽然调整可能降低了方向性风险，但如果同时增加了 gamma、theta 或 vega 风险，则可能会无意中将一种风险转换为另一种风险。

A delta adjustment made with the underlying contract is essentially a risk neutral adjustment. By this we mean that an adjustment made with the underlying contract will not change any of the other risks we have discussed because the gamma, theta, and vega associated with an underlying contract are zero. Therefore, if a trader wants to adjust his delta position, but wants to leave the other characteristics of the position unaffected, he can do so by purchasing or selling an appropriate number of underlying contracts.

使用标的合约进行的 delta 调整本质上是一个风险中性的调整。也就是说，使用标的合约进行的调整不会改变我们讨论的其他风险，因为标的合约的 gamma、theta 和 vega 都为零。因此，如果交易员想调整其 delta 头寸，但不希望影响头寸的其他特性，他可以通过买入或卖出适当数量的标的合约来实现。

An adjustment made with options may reduce the delta risk, but will also change the other risk characteristics associated with the position. Every option, in addition to having a delta, also has a gamma, theta, and vega. When an option is added to or subtracted from a position, it necessarily changes the total delta, gamma, theta, and vega of the position. This is something which new traders sometimes forget.

而通过期权进行的调整虽然可以降低 delta 风险，但也会改变与头寸相关的其他风险特性。每个期权不仅有 delta，还具有 gamma、theta 和 vega。因此，当在头寸中增加或减少一个期权时，它必然会改变头寸的总 delta、gamma、theta 和 vega，这是新手交易员有时容易忽视的点。

Consider an option market where the underlying contract is trading at 99.25. If all options appear to be overpriced, a trader might decide to sell the 95/105 strangle (sell the 95 put, sell the 105 call). Suppose the deltas of the put and call are, respectively, -36 and +36, and the trader decides to sell 20 strangles. He is initially delta neutral since

(-20 x-36) + (-20 x+30) = 0

Suppose several days pass and the underlying market has fallen to 97.00, with new delta values for the 95 put and 105 call of -41 and +30. Assuming that no adjustments have been made, the trader's delta position is now

(-20 x-41) + (-20 x+30) = +220

If the trader now decides to make an adjustment he has three basic choices:

1. sell underlying contracts
2. sell calls
3. buy puts

Which method is best?

考虑一个标的合约当前交易价格为 99.25 的期权市场。如果所有期权价格都偏高，交易员可能会选择卖出 95/105 宽跨式价差（卖出 95 认沽期权和 105 认购期权）。假设该认沽和认购期权的 delta 值分别为 -36 和 +36，而交易员决定卖出 20 份宽跨式价差组合，因此初始时他是 delta 中性的：

(-20 x -36) + (-20 x +36) = 0

假设过了几天，标的市场价格跌至 97.00，此时 95 认沽和 105 认购期权的 delta 值分别变为 -41 和 +30。如果未进行任何调整，交易员的 delta 头寸现在为：

(-20 x -41) + (-20 x +30) = +220

如果交易员现在决定进行调整，他有以下三种基本选择：

1. 卖出标的合约
2. 卖出认购期权
3. 买入认沽期权

哪种方法最好？

All other considerations being equal, whenever a trader makes an adjustment he should do so with the intention of improving the risk/reward characteristics of the position. If the trader decides to adjust his delta position by purchasing puts, he also reduces his other risks since the gamma, theta, and vega associated with the put purchase are opposite in sign to the gamma, theta, and vega associated with his existing short strangle position.

在其他条件相同的情况下，交易员进行调整时应以改善头寸的风险 / 回报特性为目标。如果交易员决定通过买入认沽期权来调整其 delta 头寸，那么这同时会降低他在 gamma、theta 和 vega 上的其他风险，因为买入的认沽期权的这些特性与他当前的宽跨式价差空头头寸的特性相反。

Unfortunately, all other considerations may not be equal. Since implied volatility can remain high or low for long periods of time, it is quite likely that if all options were overpriced when the trader initiated his position, they will still be overpriced when he goes back into the market to make his adjustment. Even though the purchase of puts to become delta neutral will reduce his other risks, such an adjustment will also have the effect of reducing the theoretical edge. On the other hand, if all options are overpriced and the trader decides to sell additional calls to reduce the delta, the sale of the overpriced calls will have the effect of increasing the theoretical edge. If the trader decides that adding to his theoretical edge is of primary importance he may decide to sell seven more 105 calls, leaving him approximately delta neutral since

(-20 x-41) + (-27 x +30) = +10

Now suppose several more days pass and the market has rebounded to 101.50, with new delta values for the 95 put and 105 call of -26 and +40. The position delta is noW

(-20 x -26) + (-27 x+40) = -560

Again, if the trader wants to adjust he is faced with three choices: buy underlying contracts, buy calls, or sell puts. Assuming that all options are still overpriced and that the trader wants to continue to increase his theoretical edge, he may decide to sell an additional 22 of the 95 puts. The total delta position is

(-42 x -26) + (-27 x +40) = +12

然而，其他条件可能并不完全相同。由于隐含波动率可能长时间维持在高或低水平，因此如果交易员在建仓时发现所有期权价格偏高，那么他回到市场进行调整时，这些期权仍然很可能偏高。虽然买入认沽期权使头寸恢复 delta 中性状态，同时降低了其他风险，但此举也会削弱理论优势。另一方面，如果所有期权价格偏高，而交易员决定通过卖出更多认购期权来减少 delta 风险，那么此操作将增加他的理论优势。如果交易员认为增加理论优势更重要，他可能会决定再卖出 7 份 105 认购期权，从而使头寸大致 delta 中性：

(-20 x -41) + (-27 x +30) = +10

假设又过了几天，市场反弹至 101.50，此时 95 认沽和 105 认购期权的 delta 值分别为 -26 和 +40。此时头寸的 delta 为：

(-20 x -26) + (-27 x +40) = -560

再次调整时，交易员有三种选择：买入标的合约、买入认购期权或卖出认沽期权。假设所有期权依然偏高，且交易员想继续增加理论优势，他可能决定再卖出 22 份 95 认沽期权。此时总 delta 头寸为：

(-42 x -26) + (-27 x +40) = +12

It should be clear what will result from these adjustments. If all options remain overpriced and the trader is always intent on increasing his theoretical edge, he will continue to make whatever adjustments are necessary by continuously selling over priced options. This method of adjusting may indeed result in the greatest profit to the trader. But notice what is happening. The strangle, which the trader was initially prepared to sell 20 times, has now increased in size to 42 × 27. If the market now makes a violent move in either direction, the negative consequences will be greatly magnified. Unfortunately, the new trader, overly concerned with always Increasing his theoretical edge, often finds himself in just such a position. If the market makes a very swift move, the trader may not survive. For this reason, a new trader who is unfamiliar with all the subtleties of an option market should avoid making adjustments which increase the size of his position.

这些调整带来的后果显而易见。如果所有期权继续偏高，而交易员一心想增加理论优势，他就会通过不断卖出偏高的期权来进行必要的调整。这种调整方式或许能带来最大收益。但要注意，此时的宽跨式价差头寸规模已经从最初的 20 份增加到了 42 × 27。如果市场出现剧烈波动，负面影响将被大幅放大。新手交易员往往过于专注于增加理论优势，却可能因此陷入这种风险之中。如果市场急速变动，交易员可能无法应对。因此，不熟悉期权市场微妙之处的新手应避免通过扩大头寸来进行调整。

No trader can afford to ignore the effect his adjustments will have on the total risk to his position. If he has a positive (negative) gamma position, buying (selling) any additional options will increase his gamma risk. Likewise, if he has a positive (negative) vega position, buying (selling) any additional options will increase his vega risk. A trader cannot afford to sell overpriced options or buy underpriced options ad infinitum. At some point the size of the spread will simply become too large, and any additional theoretical edge will have to take a back seat to risk considerations. When that happens there are only two choices: decrease the size of the spread or adjust in the underlying market.

交易员无法忽视调整对整体风险的影响。如果他有正 gamma（负 gamma）头寸，买入（卖出）额外期权将增加其 gamma 风险。同样，如果他有正 vega（负 vega）头寸，买入（卖出）额外期权会增加 vega 风险。交易员不能无限制地卖出偏高的期权或买入偏低的期权。在某个节点，头寸规模会过大，任何理论优势都要让位于风险考量。此时只有两种选择：缩小头寸规模或在标的市场中进行调整。

A disciplined trader knows that sometimes, because of risk considerations, the best course is to reduce the size of the spread, even if it means giving up some theoretical edge. This may be hard on the trader's ego, particularly if he must personally go back into the market and either buy back options which he originally sold at a lower price, or sell out options which he originally purchased at a higher price. However, if a trader is unwilling to swallow his pride from time to time, and admit that he made a mistake, his trading career is certain to be a short one.

有纪律的交易员知道，有时出于风险考虑，最好的选择是缩小头寸规模，即使这意味着要放弃一些理论优势。这对交易员的自尊可能是个挑战，尤其是在他必须重新进入市场、以比最初卖出的价格更高的价格买回期权，或者以比最初买入的价格更低的价格卖出期权时。但若交易员不肯适时放下自尊，承认错误，他的交易生涯将注定短暂。

If a trader finds that any delta adjustment in the option market that reduces his risk will also reduce his theoretical edge, and he is unwilling to give up any theoretical edge, his only recourse is to make his adjustments in the underlying market. An underlying contract has no gamma, theta, or vega, so the risks of the position will remain essentially the same.

如果交易员发现，在期权市场中任何减少风险的 delta 调整都会削弱理论优势，并且他不愿放弃理论优势，那么他唯一的选择就是在标的市场中进行调整。标的合约没有 gamma、theta 或 vega，因此头寸的风险特性将基本保持不变。

A QUESTION OF STYLE
交易风格的问题

Because most option pricing models assume that movement in the underlying contract is random, an option trader who trades purely from the theoretical values generated by a model should not have any prior opinion about the direction in which the underlying market will move. In practice, however, many option traders begin their trading careers by taking positions in the underlying market, where direction is the primary considera-tion. Many traders therefore develop a style of trading based on presumed directional moves in the underlying market. A trader might, for example, be a trend follower, adhering to the philosophy that "the trend is your friend." Or he might be a contrarian, preferring to "buy weakness, sell strength."

由于大多数期权定价模型假设标的合约的波动是随机的，因此，纯粹根据模型生成的理论价值进行交易的期权交易员，通常不会提前预测标的市场的方向。然而，许多期权交易员最初都是在标的市场中建立仓位的，方向是他们主要考虑的因素，因此形成了一种基于预期市场方向的交易风格。例如，有些交易员可能是趋势追随者，信奉 “趋势是朋友” 的理念；而有些交易员则倾向于反向操作，遵循 “买弱卖强” 的策略。

Traders often try to incorporate their personal trading styles into their option strategies. One way to do this is to consider beforehand the adjustments which will be required for a certain strategy if the underlying market begins to move. For example, suppose a trader sells straddles in such a way that he is initially delta neutral. Such spreads have a negative gamma, so that as the market moves higher his delta position is getting shorter, and as the market moves lower his delta position is getting longer. If this trader likes to trade against the trend, he will avoid adjustments as much as possible because his position is automatically trading against the trend. Whichever way the market moves, the position always wants a retracement of this movement.

交易员通常会尝试将自己的交易风格融入期权策略中。一种方法是在标的市场出现波动时，预先考虑某个策略所需的调整。例如，假设交易员通过卖出跨式价差实现初始 delta 中性。这样的价差具有负 gamma，当市场上涨时，其 delta 头寸会逐渐变短；当市场下跌时，delta 头寸会逐渐变长。如果这个交易员喜欢反向操作，他将尽量避免频繁调整，因为他的头寸已经自动与趋势相反，无论市场怎么波动，头寸总是期望价格回调。

On the other hand, a trader who sells the same straddles but prefers to trade with the trend will adjust at every opportunity. In order to remain delta neutral, he will be forced to buy underlying contracts as the market rises and sell underlying contracts as the market falls.

另一方面，如果另一位交易员也卖出相同的跨式价差，但偏好顺势交易，他将抓住每一个机会进行调整。为了保持 delta 中性，市场上涨时他将被迫买入标的合约，市场下跌时则卖出标的合约。

The opposite is true for a trader who buys straddles. He has a positive gamma position, so that as the market rises his delta is becoming longer, and as the market falls his delta is becoming shorter. If this trader likes to trade with the trend, he will want to adjust as little is possible in the belief that the market is likely to continue in the same direction. However, if he prefers to trade against the trend, he will want to adjust as often as possible. Every adjustment will represent a profit opportunity if the market does in fact reverse direction.

对于买入跨式价差的交易员情况正好相反。他的 gamma 为正，当市场上涨时，其 delta 头寸会变长；当市场下跌时，delta 头寸会变短。如果这个交易员喜欢顺势交易，他会尽量减少调整，认为市场有可能继续沿当前方向前进。然而，如果他倾向于反向交易，则会希望尽可能频繁地调整。如果市场确实反转，每次调整都将成为获利的机会。

A trader with a negative gamma is always adjusting with the trend of the underlying market. A trader with a positive gamma is always adjusting against the trend of the underlying market. If a trader prefers to trade with the trend or against the trend, he should choose a strategy and an adjustment process that is appropriate to his preference. A trader who prefers to trade with the trend can choose a strategy with a positive gamma together with less frequent adjustments, or a strategy with a negative gamma with more frequent adjustments. A trader who prefers to trade against the trend can choose a strategy with a negative gamma together with less frequent adjustments, or a strategy with a positive gamma with more frequent adjustments. The purely theoretical trader will not have to worry about this since for him there is no such thing as a trend. However, for most traders old habits, such as trading with or against the trend, die hard.

具有负 gamma 的交易员总是顺应标的市场趋势进行调整，而具有正 gamma 的交易员总是逆势调整。如果交易员倾向于顺势或逆势交易，他应选择适合该偏好的策略和调整方式。顺势交易者可以选择正 gamma 策略并减少调整频率，或选择负 gamma 策略并增加调整频率。逆势交易者可以选择负 gamma 策略并减少调整，或选择正 gamma 策略并增加调整。对于纯理论派的交易员来说，他们无需考虑趋势问题，因为在他们眼中不存在趋势。然而，对大多数交易员来说，顺势或逆势的交易习惯难以改变。

LIQUIDITY
流动性

As long as a trader has an open option position it represents a risk. Even if the risk is limited to the current value of the options, by leaving the position open the trader is risking the loss of that value. If he wants to eliminate the risk, he will have to take some action which will in effect close out the position. Sometimes this can be done through early exercise, or by taking advantage of an opposing position to create an arbitrage. More often, however, in order to close out an open position a trader will be required go into the marketplace and buy in any short options and sell out any long options.

只要交易员持有未平仓的期权头寸，就存在风险。即使风险仅限于期权的当前价值，保持头寸开放仍意味着可能损失该价值。若想消除风险，交易员必须采取措施实际平仓。通常，这可以通过提前行权或利用对立头寸进行套利实现。不过，更常见的方式是进入市场买回空头期权或卖出多头期权。

An important consideration in deciding whether to enter into a trade is often the ease with which the trader can reverse the trade. Liquid option markets, where there are many buyers and sellers, are much less risky than illiquid markets, where there are few buyers and sellers. In the same way, a spread which consists of very liquid options is much less risky than a spread which consists of one or more illiquid options. If a trader is considering entering into a spread where the options are illiquid, he ought to ask himself whether he is willing to live with that position until expiration. If the market is very illiquid, that may be the only time he will be able to get out of the position at anything resembling a fair price. If the spread consists of long-term options, say nine months, the trader may find himself married to the position for better or worse, in sickness and in health, for the next nine months. If he is unwilling to commit his capital for that period, perhaps he should avoid the position. Since there is greater risk associated with a long-term investment than with a short-term investment, a trader who does decide to take a position in long-term options ought to expect greater potential profit in the form of larger theoretical edge.

决定是否入场交易时，能否轻松反向平仓往往是关键考虑。流动性高的期权市场，买卖双方活跃，风险相对较低；而流动性差的市场，买卖双方稀少，风险较高。同理，流动性好的期权组成的价差比包含一种或多种流动性差的期权的价差风险更低。如果考虑进入流动性差的价差头寸，交易员应慎重考虑是否愿意持有至到期。如果市场极度不活跃，到期可能是唯一能以接近合理价格平仓的时机。如果价差由长期期权组成，比如九个月，交易员可能需要长期承受该头寸的起伏，如同 “婚姻” 般长期绑定。如果不愿意将资金锁定在此期间，他或许应避免该头寸。由于长期投资风险更大，交易员若选择长期期权头寸，应期待更高的理论利润作为回报。

New traders are often advised to begin trading in liquid markets. If a new trader does make an error resulting in a losing trade, in a liquid market he will be able to keep his loss to a minimum because he will be able to exit the trade with relative ease. On the other hand, an experienced trader, especially a market maker, will often prefer to deal in less liquid markets. There may be less trading activity in such markets, but the bid/ask spread is much wider, resulting in greater theoretical edge each time a trade is made. Of course, any mistake can be a problem with which the trader will have to live for a long time. However, an experienced trader is expected to keep his mistakes to a minimum.

新手通常被建议从流动性好的市场开始交易。若出现亏损交易，在流动性高的市场中，新手可以较容易平仓以减少损失。相反，经验丰富的交易员，尤其是做市商，通常更愿意在流动性较差的市场中操作。虽然这类市场的交易活跃度较低，但买卖价差更宽，每次交易都能获得更大的理论收益。当然，犯错的代价可能持续很久，但有经验的交易员应能最大限度减少错误。

The most liquid options in any market are those which are short-term and which are either at or slightly out-of-the-money. Such options always have the narrowest bid/ask spread, and there are usually traders willing to buy or sell large numbers of these contracts. As a trader moves to longer term options, or to options which are more deeply in-the-money, he finds that the bid/ask spread begins to widen, and there are fewer and fewer traders interested in these contracts. While at-the-money short-term options are constantly traded, deeply in-the-money long-term options may not trade for weeks at a time.

任何市场中流动性最好的期权是短期、在价内或轻微价外的期权。这些期权的买卖价差最窄，通常有大量交易员愿意买入或卖出这些合约。当交易员选择较长期的期权或深度价内的期权时，买卖价差会扩大，感兴趣的交易员也越来越少。与短期平价期权频繁交易相比，深度价内的长期期权可能数周内都没有交易。

In addition to the liquidity of an option market, a trader should also give some thought to the liquidity of the underlying market. If a trader has an option position and wants to make an adjustment, he may find it difficult to do if the option market is illiquid. If the underlying market is liquid, he will at least he be able to make his adjustment in that market with relative ease. The most dangerous market in which to trade is one where both the options and the underlying contract are inactively traded. Only the most experienced and knowledgeable traders should enter such markets.

除了期权市场的流动性，交易员还应考虑标的市场的流动性。如果期权市场流动性较差，但标的市场流动性充足，至少可以相对容易地在标的市场进行调整。最具风险的市场是那些期权和标的合约都不活跃的市场，仅适合最具经验和知识的交易员进入。

End-of-day volume figures and bid/ ask spreads in S&p 500 index options traded at the Chicago Board Options Exchange on July 9, 1993 are shown in Figure 9-15. Note the lower volume and wider bid/ask spread for back month and deeply in-the-money options, versus front month and at- and out-of-the-money options.

图 9-15 显示了 1993 年 7 月 9 日在芝加哥期权交易所交易的 S&P 500 指数期权的收盘成交量和买卖价差。请注意远月和深度价内期权的较低成交量和较宽买卖价差，相比之下，近月以及平价和价外期权的流动性更好。