Chapter 7 Introduction to Spreading
第七章 价差交易简介
In option markets, as in all markets, there are many ways to trade profitably. One type of trading strategy, common among floor traders, is scalping. A scalper attempts to buy at the bid price and sell at the offer price as often as possible, without regard to the contract's theoretical value. Although the profit from each trade may be small, if a trader can do this enough times each day he can expect to show a reasonable profit. Scalping, however, requires a highly liquid market, and option markets are rarely sufficiently liquid to support this type of trading.
在期权市场中，与所有市场一样，有多种盈利的交易方式。其中一种常见于场内交易员的策略是“剥头皮”交易。剥头皮交易员会尽可能多次以买入价买入、以卖出价卖出，而不考虑合约的理论价值。尽管每次交易利润较小，但如果交易员每天重复足够多次，仍有可能获得合理的收益。然而，剥头皮交易需要极高的市场流动性，而期权市场通常不具备足够的流动性来支持此类交易。
A different type of trading strategy involves speculating on the direction in which the underlying contract will move. If a speculator correctly anticipates the market direction, and takes an appropriate position, he can also expect to show a profit. But even when the market moves in the expected direction, taking a directional position in an option market will not necessarily be profitable. Many different forces beyond directional considerations can affect an option's price. If a trader's sole consideration is direction, he will usually be better off taking a position in the underlying market. If he does, and he is right, he is assured of making a profit.
另一种策略是对标的合约价格的走势进行方向性投机。如果投机者正确预测市场方向并建立相应头寸，也有机会获利。但即使市场走势如预期，在期权市场中采取方向性头寸也不一定能带来收益。期权价格受多种因素影响，超出单纯的方向性考量。如果交易员仅关注方向，通常直接在市场建立头寸会更有利。如果预测正确，便可确保获利。
The majority of successful option traders engage in spread trading. Since option evaluation is based on the laws of probability, and because the laws of probability can be expected to even out only over long periods of time, option traders must often hold positions for extended periods. Unfortunately, over short periods of time, while the trader is waiting for the option price to move towards theoretical value, the trader may be at risk from a wide variety of changes in market conditions which threaten his potential profit. Indeed, over short periods of time there is no guarantee that an option will react in a manner consistent with a theoretical pricing model. Spreading is simply a way of enabling an option trader to take advantage of theoretically mispriced options, while at the same time reducing the effects of short-term changes in market conditions so that he can safely hold an option position to maturity.
大多数成功的期权交易员采用价差交易。由于期权定价基于概率法则，而概率的均衡通常只有在较长时间内才显现，期权交易员往往需要持有头寸一段时间。然而，在短期内，当交易员等待期权价格向理论价值回归时，可能面临多种市场条件变化的风险，威胁其潜在收益。实际上，在短期内，期权未必会如理论定价模型所预测的那样反应。价差交易正是通过利用理论上价格偏离的期权，同时降低短期市场条件变化的影响，从而使交易员能更安全地持有期权头寸直至到期。
WHAT IS A SPREAD?
什么是价差交易？
A spread is a strategy which involves taking simultaneous but opposing positions in different instruments. A spread trader makes the assumption that there is an identifiable price relationship between different instruments and, although he may not know in which direction the market will move, the price relationship between the instruments ought to remain relatively constant. When the relationship appears to be temporarily mispriced, the spread trader will take a long position in the instruments which appears to be underpriced and a short position in the instrument which appears to be overpriced. The trader hopes to profit when the prices of the instruments return to their expected relationship.
价差交易是一种同时在不同工具上建立相反头寸的策略。价差交易者假设这些工具之间存在可以识别的价格关系，虽然他可能无法预测市场的具体方向，但这些工具之间的价格关系应该保持相对稳定。当这种关系短暂失衡时，交易者会对被低估的工具建立多头头寸，对被高估的工具建立空头头寸。交易者希望当这些工具的价格回归到预期关系时获利。
Among futures traders the most common type of spread involves taking positions in different delivery months for the same commodity, A trader might purchase October crude oil and sell November crude oil on the New York Mercantile Exchange. Or he might buy December corn and sell July corn on the Chicago Board of Trade. The value of this type of intra-market spread depends on a variety of factors, the most important of which is usually the cost of carrying the physical commodity from one delivery month to another.
在期货交易者中，最常见的价差交易类型是对同一商品的不同交割月份建立头寸。例如，交易者可能在纽约商业交易所买入10月原油合约，同时卖出11月原油合约，或在芝加哥期货交易所买入12月玉米合约并卖出7月玉米合约。这种市场内价差的价值依赖多种因素，其中最重要的通常是将实物商品从一个交割月份保存到另一个交割月份的持有成本。
Suppose that February gold on the COMEX is trading for $360 per ounce. What should April gold be trading for? A trader who takes delivery of gold in February at $360 per ounce and holds it until April will incur a debit of $360 per ounce for a two-month period. If interest rates are 9 percent annually, the two-month financing cost will be:
9% × 2/12 × $360 = $5.40
假设纽约商品交易所的2月黄金期货交易价格为每盎司360美元。那么4月的黄金期货应该是什么价格？若交易者在2月以360美元每盎司买入黄金并持有到4月，将产生为期两个月的360美元每盎司的借贷成本。如果年利率为9%，两个月的融资成本为：
9% × 2/12 × $360 = $5.40
Given the financing cost of $5.40 per ounce that can be saved by purchasing an April futures contract rather than purchasing the physical commodity, the April contract ought to be worth $5.40 more than the February contract, or $365.40 per ounce. If the February contract is trading at $360 and the April contract is trading at $364, the trader knows that the spread is $1.40 too cheap. He can profit from this mispricing by purchasing the spread for $4.00 (buy April for $364, sell February for $360). If the spread returns to its expected value of $5.40, the trader can buy back the February contract and sell out the April contract, thereby realizing a profit of $1.40.
考虑到通过购买4月期货合约而不是实物商品可以节省的5.40美元融资成本，4月合约应比2月合约高5.40美元，即每盎司365.40美元。如果2月合约交易价格为360美元，而4月合约为364美元，交易者就知道该价差比预期便宜1.40美元。他可以通过以4.00美元的价差买入（以364美元买入4月合约，同时以360美元卖出2月合约）从中获利。如果价差回到预期的5.40美元，交易者可以回购2月合约并卖出4月合约，实现1.40美元的利润。
Note that the above spread will be profitable regardless of the general direction of the gold market, as long as the prices of the two delivery months return to their expected $5.40 spread. If February gold rises to $370, the trader will lose $6 on the February side of his spread. If, however, the April contract rises to $375.40, the gain in the value of the April contract will more than offset the loss on the February contract and result in the expected $1.40 per ounce profit.
请注意，只要2月和4月黄金合约的价差回到预期的5.40美元，不论黄金市场整体价格走势如何，这一价差交易都能盈利。如果2月黄金涨至370美元，交易者在2月合约上的损失为6美元。但如果4月合约涨至375.40美元，4月合约的增值会超过2月合约的损失，从而实现每盎司1.40美元的预期利润。
Factors other than financing costs can also affect the price relationship between different futures months for the same commodity. The futures price of some commodities must also include the cost of storing and insuring the commodity for the period between delivery months. In theory, the cost of financing, storing, and insuring a traditional commodity (precious metals, agricultural products, livestock, energy products, etc.) must be some positive number, so that the price of a more distant delivery month ought to be greater than the price of a nearby delivery month. This is known as a contango relationship. Any increase in these costs will increase the value of a futures contract.
除融资成本外，其他因素也会影响同一商品在不同期货交割月份的价格关系。例如，一些商品的期货价格还需考虑从一个交割月到下一个交割月期间的储存和保险成本。理论上，传统商品（如贵金属、农产品、牲畜、能源产品等）的融资、储存和保险成本总是正数，因此远月合约价格应高于近月合约价格，这种关系被称为正向市场。这些成本的增加会提高期货合约的价值。
Supply and demand considerations can also affect the spread relationship of different delivery months. In theory, a November crude oil contract ought to always trade for more than an October crude oil contract. But if crude oil is currently in short supply, refiners may be willing to pay more for an October futures contract in order to ensure an uninterrupted flow of crude oil to their refineries. Markets where the near-by delivery month is trading at a premium to the more distant months are said to be in backwardation. Supply and demand for raw materials can often cause traditional commodities markets to go into backwardation. Examples of contango and backwardation markets are shown in Figure 7-1.
供需因素也会影响不同交割月份的价差关系。理论上，11月原油合约应始终高于10月原油合约。但如果当前原油供应紧缺，炼油商可能愿意支付更高的价格购买10月期货合约，以确保炼油厂的原油供应无中断。当近月合约价格高于远月合约价格时，这种市场被称为逆向市场。原材料的供需常导致传统商品市场进入逆向状态。图7-1展示了正向市场和逆向市场的示例。
| Contago Markets | |||||||
|---|---|---|---|---|---|---|---|
| Month | Open | High | Low | Settle | Change | Lifetime High | Lifetime Low |
| Friday, October 22, 1993 | |||||||
| OCOA (CSCE); 10 metric tons; $ per metric ton. (1 = $10.00) | |||||||
| Dec | 1163 | 1166 | 1125 | 1134 | -21 | 1506 | 919 |
| Mar94 | 1200 | 1203 | 1161 | 1174 | -20 | 1495 | 835 |
| May | 1215 | 1215 | 1172 | 1183 | -24 | 1518 | 841 |
| Jul | 1226 | 1226 | 1190 | 1200 | -23 | 1530 | 845 |
| Sep | 1237 | 1237 | 1220 | 1220 | -20 | 1536 | 878 |
| Mar95 | 1239 | 1239 | 1239 | 1239 | -20 | 1346 | 980 |
| COTTON (CTN); 50,000 lbs.; ¢ per lb. (.01 = $5.00) | |||||||
| Dec | 1163 | 1166 | 1125 | 1134 | -21 | 1506 | 919 |
| Mar94 | 1200 | 1203 | 1161 | 1174 | -20 | 1495 | 835 |
| May | 1215 | 1215 | 1172 | 1183 | -24 | 1518 | 841 |
| Jul | 1226 | 1226 | 1190 | 1200 | -23 | 1530 | 845 |
| Oct | 1237 | 1237 | 1220 | 1220 | -20 | 1536 | 878 |
| Dec | 1239 | 1239 | 1239 | 1239 | -20 | 1346 | 980 |
| SOYBEAN MEAL (CBT); 100 tons; $ per ton. ( .01 = $10.00) | |||||||
| Dec | 193.30 | 194.60 | 192.90 | 193.10 | -.30 | 235.50 | 183.40 |
| Jan | 193.30 |
194.70 | 193.10 | 193.40 | .... |
231.50 | 176.90 |
| Mar | 194.30 | 195.90 | 194.30 | 194.40 | -.10 | 231.00 | 175.60 |
| May | 196.00 | 197.00 | 195.40 | 195.40 | +.40 |
228.00 | 177.00 |
| Jul | 197.50 | 198.70 | 197.20 | 197.40 | +.10 | 245.00 | 179.00 |
| Aug | 197.50 | 198.40 | 197.50 | 197.50 | .... | 237.50 | 180.10 |
| Backwardation Markets | |||||||
|---|---|---|---|---|---|---|---|
| Month | Open | High | Low | Settle | Change | Lifetime High | Lifetime Low |
| Monday, December 10, 1990 | |||||||
| CATTLE (CME); 44,000 lbs.; ¢ per lb. (.01 = $4.40) | |||||||
| Dec | 79.97 | 80.75 | 79.97 | 80.70 | +.78 | 79.77 | 71.00 |
| Feb91 | 76.35 | 77.00 | 76.25 | 76.87 | +.70 | 77.80 | 72.50 |
| Apr | 76.20 | 76.95 | 76.20 | 76.87 | +.65 | 78.05 | 74.00 |
| Jun | 74.10 | 74.65 | 74.10 | 74.55 | +.50 | 75.45 | 72.15 |
| Aug | 72.70 | 73.12 | 72.70 | 72.92 | +.35 | 73.85 | 70.35 |
| Oct | 72.70 | 73.05 | 72.70 | 72.90 | +.48 | 72.85 | 70.70 |
| COPPER (COMEX); 25,000 lbs.; ¢ per lb. (.01 = $2.50) | |||||||
| Jan | 110.00 | 110.85 | 109.60 | 110.80 | +1.30 | 126.40 | 91.50 |
| Feb | 109.00 | 109.80 | 108.90 | 109.80 | +1.60 | 115.80 | 99.50 |
| Mar | 106.40 | 108.40 | 106.30 | 108.00 | +2.00 | 122.60 | 92.30 |
| Apr | 106.00 | 108.00 | 106.00 | 107.20 | +2.00 | 115.50 | 99.85 |
| May | 105.15 | 106.70 | 105.00 | 106.40 | +2.05 | 117.80 | 97.00 |
| Jul | 103.80 | 105.30 | 103.80 | 104.80 | +2.10 | 110.50 | 95.50 |
| HEATING OIL (NYMEX); 42,000 gallons; ¢ per gallon (.01 = $4.20) | |||||||
| Jan | 81.60 | 82.50 | 80.80 | 80.97 | +1.80 | 107.25 | 52.95 |
| Feb | 79.00 | 79.20 | 77.60 | 77.76 | +1.52 | 102.00 | 52.60 |
| Mar | 74.00 | 74.00 | 72.70 | 72.82 | +.81 | 96.50 | 50.70 |
| Apr | 69.50 | 69.50 | 68.10 | 68.12 | +.46 | 92.00 | 49.30 |
| May | 66.20 | 66.25 | 65.90 | 66.12 | +.11 | 88.50 | 48.40 |
| Jun | 64.75 | 64.75 | 64.00 | 63.22 | -.14 | 85.75 | 48.40 |
The cost of carrying a position in an underlying commodity is only one of many factors which can affect a futures spread relationship. A trader who purchases a stock index futures contract will save the financing costs associated with owning the basket of stocks which make up the index. At the same time, he gives up the rights to any dividends he might receive if he actually owned the stocks. The savings in financing costs add value to the futures contract, but the loss in dividends reduces the contract's value. (footnote 1: Because of their unique importance in financial markets, we will look at stock index futures and options in detail in Chapter 15.)
持有标的商品头寸的成本只是影响期货价差关系的众多因素之一。交易者购买股指期货合约可节省持有构成该指数的股票组合的融资成本，但同时也失去了实际持有股票时可获得的股息权利。融资成本的节省增加了期货合约的价值，而股息的损失则减少了合约的价值。（脚注1：由于其在金融市场中的独特重要性，我们将在第15章详细讨论股指期货和期权。）
Matters can be further complicated if different interest rates play a role in the evaluation of a spread relationship. The value of a treasury bond futures contract depends not only on the carrying costs saved by purchasing a futures contract instead of the actual bond (the short-term rate), but also on the interest lost by not owning the bond (the long-term rate). Depending on the difference between short and long-term rates, distant delivery months in the treasury bond futures market can be trading at either a premium to the nearby months or at a discount to the nearby months. Similar types of considerations affect relationships in foreign currency futures markets, but here the determining factors are the difference between domestic and foreign interest rates. When foreign rates are low compared to domestic rates, the more distant months trade at a premium; when foreign rates are high, the more distant months trade at a discount.
如果不同的利率在价差关系中起作用，情况会更加复杂。国债期货合约的价值不仅取决于购买期货合约而非实际债券所节省的持有成本（短期利率），还取决于未持有债券而损失的利息（长期利率）。根据长短期利率的差异，远月国债期货合约的价格可能高于近月合约，也可能低于近月合约。类似的因素也影响外汇期货市场的价差关系，但关键因素在于国内外利率差异。当外币利率低于国内利率时，远月合约通常溢价交易；当外币利率高时，远月合约则通常折价交易。
Calculating the spread relationship between different delivery months can be a complex problem, and is covered more fully in texts focusing specifically on futures trading. The point here is that, in theory, there ought to be a well defined price relationship between different delivery months. When this relationship is violated in the marketplace, a potential profit opportunity exists by selling the overpriced contract and buying the underpriced.
计算不同交割月份之间的价差关系较为复杂，更多细节在专注期货交易的书籍中有详细探讨。这里的重点在于，理论上不同交割月份之间应该存在明确的价格关系。当市场上这种关系被打破时，可以通过卖出高估合约并买入低估合约来获取潜在利润。
Spreads need not be based solely on the relationship between different delivery months for the same commodity. They can also be based on presumed price relationships between different, though usually related, instruments. The NOB (notes over bonds) spread traded on the Chicago Board of Trade is based on the assumption that there is an identifiable relationship between the price of Treasury Bonds and Treasury Notes. When the spread between the prices of these two futures contracts is more or less than expected, traders will sell one instrument and buy the other. For example, with Treasury Notes at 99-16 (footnote 2: U.S. Treasury Bonds and Notes are traded in points and 32nds. 99-16 represents a price of 99 16/32.) and Treasury Bonds at 96-00, there is a 3-16 spread between the two instruments. If a trader feels, based on his analysis of interest rates, that the spread between Notes and Bonds ought to be 3-00, he can sell the spread at 3-16 (sell Notes at 99-16, buy Bonds at 96-00). If the spread returns to its expected value of 3-00, the trader can buy in his Notes and sell out his Bonds, realizing a profit of 16/32.
价差交易不一定只基于同一商品在不同交割月份的关系，也可以基于不同但通常相关的合约之间的价格关系。芝加哥期货交易所交易的NOB（短期国债对长期国债）价差交易就是基于国债和国库券之间存在的价格关系。当这两者的期货合约价差高于或低于预期时，交易者会卖出一种合约并买入另一种合约。例如，当国库券价格为99-16时（脚注2：美国国债和国库券以点数和32分之一计价。99-16表示价格为99又16/32。），国债价格为96-00，两者价差为3-16。如果交易者基于利率分析认为国库券和国债的价差应为3-00，他可以在3-16卖出价差（卖出99-16的国库券，买入96-00的国债）。当价差回归预期的3-00时，交易者可以买回国库券并卖出国债，从而实现16/32的利润。
Spreads can also be based on more complex relationships. Many traders on the COMEX follow the price relationship between gold and silver. However, with gold at $300 to $400 per ounce and silver at $4 to $5 per ounce (as of this writing), the relationship is more commonly expressed as a ratio. Suppose a trader decides that the spread between the two metals ought to be 80 ounces of silver to one ounce of gold (an 80:1 ratio). If silver is trading at $4.50, given the 80:1 price ratio, gold ought to be trading at $4.50 x 80 = $360. If, however, gold is at $375, the spread trader will sell one ounce of gold at $375, and buy 80 ounces of silver at $4.50. Regardless of the general trend in prices of precious metals, he expects to make $15 when the spread returns to its 80:1 ratio. If the precious metals market drops, so that gold is at $336 and silver is at $4.20 (the expected 80:1 ratio), the trader's total profit will be:
80 × ($4.20 - $4.50) = -$24 (silver)
$375 - $336 = +$39 (gold)
As expected, he has shown a profit of $15.
价差交易也可以基于更复杂的关系。许多COMEX交易者关注黄金和白银的价格关系。由于黄金每盎司在300至400美元之间，而白银每盎司在4至5美元之间（撰写时的数据），通常用比率表示这种关系。假设一位交易者认为两者的价差应为80盎司银兑1盎司金（80:1的比率）。如果白银价格为4.50美元，那么按80:1的价格比率，黄金价格应为4.50 × 80 = 360美元。但如果黄金价格为375美元，价差交易者会在375美元卖出1盎司黄金，同时在4.50美元买入80盎司白银。无论贵金属价格整体趋势如何，当价差回到80:1时，他预期会获利15美元。如果贵金属市场下跌，黄金降至336美元，白银降至4.20美元（符合预期的80:1比率），交易者的总利润为：
80 × (4.20 - 4.50) = -24美元（白银）
375 - 336 = +39美元（黄金）
如预期，最终利润为15美元。
Spreads can also reflect a trader's opinion that one contract will outperform a different contract. Futures on the New York Stock Exchange Composite Index traded on the New York Futures Exchange represent the value of approximately 1500 actively traded stocks. Futures on the Standard & Poor's 500 Index traded on the Chicago Mercantile Exchange represent the value of 500 such stocks. If a trader believes the relationship between the two index values ought to be 9 to 5 (9 NYSE = 4 S&P 500), and the current prices are 220 and 396, the price relationship is, as expected, 9:5 (9 x 220 = 5 × 396). There does not seem to be any reason to either buy or sell the spread. If, however, a trader believes that in percent terms the 500 stocks in the S&P will outperform the 1500 stocks in the NYSE, he can buy five S&P contracts and sell nine NYSE contracts. If, in percent terms, the S&P rises more quickly, or declines less quickly, the trader will profit from the better performance of the contracts which he owns.
价差交易也可以反映交易者对不同合约表现的预期。纽约期货交易所的纽约证券交易所综合指数期货代表约1500只活跃交易的股票，而芝加哥商业交易所的标准普尔500指数期货代表500只股票的价值。如果交易者认为两者的关系应为9比5（9倍NYSE = 5倍S&P 500），且当前价格分别为220和396，那么价格关系确实是9:5（9 × 220 = 5 × 396）。此时没有理由买入或卖出该价差。然而，如果交易者认为标准普尔500指数的500只股票在涨跌幅上将优于纽约证券交易所的1500只股票，他可以买入5张标准普尔合约，卖出9张纽约证券交易所合约。若标准普尔指数上升更快或下跌更慢，交易者将从所持合约的更好表现中获利。
Spread relationships need not be restricted to two instruments. Sometimes three, or even more, different instruments may define a spread relationship. We calculated that if February gold is at $360, and interest rates are 9%, the spread between February and April gold ought to be $5.40. If interest rates rise, the carrying costs will also rise, and the February/April spread will widen. If a trader is long February gold and short April gold, and he feels that Eurodollar interest rates correlate closely to his cost of carry, he can sell Eurodollar futures to protect himself against a rise in interest rates. If interest rates do rise, he will lose on his February/April spread, but this will be offset by the profit on his Eurodollar position. He has made the assumption that there is a three-sided spread relationship between the price of February gold, April gold, and Eurodollars.
价差关系不限于两种工具，有时甚至涉及三种或更多工具。我们计算得出，如果2月黄金价格为360美元，利率为9%，则2月和4月黄金之间的价差应为5.40美元。如果利率上升，持仓成本也会上升，2月/4月价差会扩大。如果交易者持有2月黄金的多头、4月黄金的空头，且认为欧洲美元利率与他的持仓成本密切相关，他可以卖出欧洲美元期货来防范利率上升。当利率上升时，2月/4月黄金价差损失将由欧洲美元头寸的获利来抵消。他假设2月黄金、4月黄金和欧洲美元之间存在一个三方价差关系。
Much of the most sophisticated trading in derivative markets involves identifying and following spread relationships. When a trader decides that a spread relationship is mispriced in the marketplace, it can be just as profitable to buy or sell the spread as to take an outright long or short position in a single instrument.
在衍生品市场中，识别并跟踪价差关系是高阶交易策略之一。当交易者发现市场中价差关系出现错误定价时，买入或卖出该价差可能与直接持有单一工具的多头或空头头寸一样获利。
In the forgoing examples the price relationship between instruments was defined in point or currency terms. In some cases, however, it may be more practical to define the relationship in other terms. In Chapter 4 we used theoretical pricing model to determine an option's implied volatility, and we noted that for an option trader the implied volatility might be a more accurate reflection of an option's price than its dollar price. An option trader might therefore express the spread value between two options in terms of the spread between their implied volatilities. An option with an implied volatility of 15% and a different option with an implied volatility of 17% have a two-point volatility spread, regardless of the difference in their dollar prices. If both options have the same underlying instrument, a trader might purchase the option with an implied volatility of 15% and sell the option with an implied volatility of 17%, hoping to profit when the spread between the implied volatilities narrows.
在上述例子中，工具间的价格关系用点数或货币表示。然而，在某些情况下，可能更实用的是以其他指标定义关系。在第4章中，我们使用理论定价模型确定期权的隐含波动率，并指出对期权交易者而言，隐含波动率可能比美元价格更能准确反映期权价值。因此，期权交易者可以用两个期权的隐含波动率之差来表示价差。例如，一个期权的隐含波动率为15%，另一个为17%，则波动率价差为两个百分点，无论它们的美元价格差异。如果两者基于相同的标的资产，交易者可以买入隐含波动率为15%的期权并卖出隐含波动率为17%的期权，期望当隐含波动率差缩小时获利。
As we shall see, the foregoing example is simplistic. An option trader cannot simply buy options with low implied volatilities and sell options with high implied volatilities. Not only is the spread between implied volatilities important, but also the general level of implied volatility. A two-percentage-point volatility spread may mean one thing if the implied volatilities are 0% and 8%, and something else if the implied volatilities are 26% and 28%. Moreover, there are important considerations of risk arising from difficulties in predicting volatility, as well as the possible inaccuracies in the models themselves. In spite of these factors, volatility spreads form one of the most important classes of option trading strategies. Much of an option trader's education is spent studying volatility relationships, and learning to create spreads based on mispriced volatility.
正如我们将看到的，以上例子过于简单。期权交易者不能单纯买入隐含波动率低的期权并卖出隐含波动率高的期权，不仅需要关注隐含波动率的价差，还需考虑总体隐含波动率水平。当隐含波动率为0%和8%时，两个百分点的波动率价差意义可能与26%和28%时不同。此外，由于波动率预测难度和模型可能的误差，风险因素同样重要。尽管如此，波动率价差仍然是期权交易中重要的策略之一。期权交易者的许多学习内容集中在研究波动率关系，并创建基于错误定价波动率的价差策略。
In the previous examples we assumed that a spreading strategy was static, that once the spread was initiated it was only necessary to wait for the spread to reach its expected value. Spreads can also be dynamic, requiring action over the life of the spread in order to profit from the mispricing. This was the method used in Chapter 5 to take advantage of a mispriced option. The option was spread against the underlying contract, and the position was adjusted over the life of the option. At expiration, the resulting profit was approximately equal to the amount by which the option was originally mispriced.
在之前的例子中，我们假设价差策略是静态的，即一旦建立价差，只需等待其达到预期值。然而，价差也可以是动态的，需要在价差存续期内进行调整，以从错误定价中获利。这是第5章中用以利用期权错误定价的方法，期权与其标的合约之间建立价差，并在期权存续期间进行调整，最终在到期时获得的收益约等于期权初始的错误定价金额。
WHY SPREAD?
为什么做价差交易？
We saw in Chapter 3 that most theoretical pricing models depend on the laws of probability to generate option values. Even if we have correctly estimated the prob-abilities, i.e., volatility, we know that probability theory is only valid over many occurrences or, in the case of options, over long periods of time. A trader will sometimes have to hold an option position for an extended period in order to profit from the option's mispricing. Unfortunately, while he is holding the position, over short periods of time he may have to put up with adverse fluctuations in the position's value. The fluctuations might be severe enough that the trader, because of capital requirements, will not be able to maintain the position. If he is forced to liquidate the position prior to expiration, there is no guarantee that he will profit from the option's mispricing, even if he has accurately estimated all the inputs into the pricing model. By spreading, a trader is attempting to reduce the effect of short-term "bad luck" that goes with any investment based on the laws of probability.
在第3章中我们看到，大多数理论定价模型依赖概率法则来生成期权的价值。即使我们准确估算了概率（即波动率），也知道概率理论仅在多次发生或较长时间内才有效。在期权交易中，交易者有时需要持有头寸较长时间，才能从期权的错误定价中获利。但在此期间，头寸价值可能会受到不利波动，若波动过大，可能会因资本要求而无法维持头寸。如果交易者被迫提前平仓，即便所有定价模型输入值都是准确的，也无法保证获利。通过价差交易，交易者尝试减少任何基于概率的投资所面临的短期“运气不佳”的影响。
Spreading strategies not only take advantage of the laws of probability by enabling a trader to hold option positions over long periods of time, but such strategies also have the effect of protecting the trader against incorrectly estimated inputs into the theoretical pricing model. Suppose a trader estimates that over the life of an option the volatility of an underlying Deutschemark futures contract will be 13%. Based on this estimate he finds that a certain call trading at the Chicago Mercantile Exchange has a theoretical value of 1.75 but is actually trading for 2.00. If the call has a delta of 25, one strategy is to sell four calls for 2.00 each and buy one futures contract, yielding a theoretical edge of 4 x .25 = 1.00, or $1,250. (Each point in currency contracts at the Chicago Mercantile Exchange is worth $1,250.) Of course, if the trader can make $1,250 with a 4 x 1 spread, it may occur to him that he can make $12,500 if he increases the size of the spread to 40 x 10. Why stop now? He can make $125,000 if he increases the size to 400 × 100.
价差策略不仅通过允许交易者长时间持有期权头寸来利用概率法则，同时还能在理论定价模型输入值估算不准时为交易者提供保护。假设某交易者估计期权存续期间德马克期货合约的波动率为13%，基于此估计，他发现芝加哥商业交易所的一份看涨期权理论价值为1.75，但实际交易价为2.00。若该期权的delta值为25，一种策略是以2.00的价格卖出4份看涨期权，同时买入1份期货合约，形成4 x 0.25 = 1.00的理论优势，即$1,250（芝加哥商业交易所的每一点货币合约价值$1,250）。当然，如果交易者通过4 x 1的价差可以赚$1,250，那么他可能会考虑扩大到40 x 10，从而赚$12,500。再进一步，若扩大至400 x 100，便可赚到$125,000。
Even if the market is sufficiently liquid to absorb unlimited size, is this a reasonable approach to trading? Should a trader simply find a theoretically profitable strategy and do it as many times as possible in order to maximize the profit potential? At some point the intelligent trader will have to consider not only the potential profit, but also the risk associated with a strategy. After all, his volatility estimate of 13% is just that, an estimate. What will happen if volatility actually turns out to be some higher number, perhaps 15%, or 17%? If the calls which he sold at 2.00 are worth 2.25 at a volatility of 17%, and volatility actually turns out to be 17%, then his hoped-for profit of $125,000 (assuming a size of 400 x 100) will turn into a loss of $125,000.
即使市场有足够的流动性来吸收无限量的交易，这样的做法合理吗？交易者是否应当只找到一个理论上有利可图的策略，并无限次执行以最大化利润？聪明的交易者在某个节点需要考虑的不仅是潜在利润，还有策略的风险。毕竟，他对13%的波动率只是个估计。如果实际波动率更高，比如15%或17%，会怎样？如果波动率达到17%，而他以2.00卖出的看涨期权变成了2.25，那么原本希望赚取的$125,000利润（假设400 x 100规模）将变成亏损$125,000。
A trader must always consider the effects of an incorrect estimate, and then decide how much risk he is willing to take. If the trader in this example decides that he can survive if volatility goes no higher than 15% (a two-percentage-point margin for error), he might only be willing to do the spread 40 x 10. But if there were some way to increase his break-even volatility to 19% (a six-percentage-point margin for error), he might indeed be willing to do the spread 400 x 100. Option spreading strategies enable traders to profit over a wide variety of market conditions by giving them an increased margin for error in estimating the inputs into a theoretical pricing model. No trader will survive very long if his livelihood depends on estimating each input with 100% accuracy. Even when he incorrectly estimates the inputs, the experienced trader can survive if he has constructed intelligent spread strategies which allow for a wide margin of error.
交易者必须始终考虑估算错误的影响，并决定愿意承担的风险程度。假设这个例子的交易者认为波动率若不超过15%他可以接受（即有2%的误差空间），那么他可能只愿意做40 x 10的价差。但如果有办法将其盈亏平衡点的波动率提高至19%（6%的误差空间），他可能会考虑做400 x 100的价差。期权价差策略让交易者在多种市场条件下获利，同时扩大了理论定价模型输入估计的误差容忍度。若交易完全依赖每个输入的100%准确性，交易者很难长久生存。但即便估算出错，若采用合理的价差策略，经验丰富的交易者依然可以在广泛的误差范围内生存下去。
SPREADING AS A RISK MANAGEMENT TOOL
风险管理中的价差
Recall our example in Chapter 3 where a casino is selling a roulette bet with an expected return of 95¢ (American conditions) for $1.00. The casino owner knows that based on the laws of probability he has 5% theoretical edge. Suppose that one day a bettor comes into the casino and proposes to bet $2,000 on one number at the roulette table. The casino owner knows that the odds are on his side and that he will most likely get to keep the $2,000 bet. But there is always a chance that the player will win, and that the casino will lose $70,000 (the $72,000 payoff less the $2,000 cost of the bet) if the player's number does come up.
回忆一下我们在第三章中的例子：赌场以1美元出售轮盘赌的投注，预期回报为0.95美元（基于美式规则）。赌场老板知道，根据概率法则，他有5%的理论优势。假设有一天，一个赌客进入赌场，提议在轮盘赌上押2000美元在某个号码上。赌场老板知道赔率对自己有利，很可能会赢下这笔2000美元的赌注。但如果这个赌客押中的号码真的出现，赌场将会损失7万美元（7.2万美元的奖金减去赌注的2000美元）。
Now suppose that two other bettors come into the casino, and each proposes to place a $1,000 bet at the roulette table. They promise, however, to bet on different numbers. Whichever number one bettor chooses, the other bettor will choose some other number. As with the first bettor and his single bet of $2,000, the casino's potential reward in this new scenario is also $2,000, if neither of the two numbers come up. But the risk to the casino is now only $34,000 (the $36,000 payoff if one player wins, less the cost of the two $1,000 bets). Since only one player can win, the two bets are mutually exclusive: if one wins, the other must lose.
假设接下来又有两个赌客来到赌场，分别在不同的号码上各押1000美元。无论一个赌客选择哪个号码，另一个赌客都会选择不同的号码。与第一个赌客在单一号码上押2000美元的情况相同，赌场在这种新情况下的潜在收益仍是2000美元（如果两个号码都未中）。但赌场的风险则减少为3.4万美元（如果其中一人赢了，奖金为3.6万美元，减去两个1000美元的赌注成本）。由于两个赌注互相排斥：若一个赢，另一个必输。
Given our two scenarios, one bettor wagering $2,000 on one number, or two players wagering $1,000 each on different numbers, what is the theoretical edge to the casino? The edge to the casino in both cases is still the same 5%. Regardless of the amount wagered, or the number of individual bets, the laws of probability say that in the long run the casino gets to keep 5% of everything that is bet at the roulette table. In the short run, however, the risk to the casino is greatly reduced with two $1,000 bets because the bets have been spread around the table.
在这两种情况下，一个赌客在单个号码上押2000美元，或两个赌客在不同号码上各押1000美元，赌场的理论优势仍是5%。无论赌资金额大小或赌注数量，概率法则都说明，从长远看，赌场可保留轮盘赌投注额的5%。然而在短期内，因投注分散在不同号码上，赌场的风险大大降低。
A casino does not like to see a bettor wager a large amount of money on one outcome, whether at roulette or any other casino game. The odds are still in the casino's favor. But, if the bet is large enough, and the bettor is lucky, short-term bad luck can overwhelm the casino. Indeed, if a bettor knows that the odds are against him, and he wants the greatest chance of showing a profit, his best course is to wager the maximum amount on one outcome, and hope that in the short run he gets lucky. If he continues to make bets over a long period of time, the laws of probability will eventually catch up with him and the casino will end up with the bettor's money. The ideal scenario from the casino's point of view is for 38 players to place 38 bets of $1,000 each on all 38 numbers at the roulette table. Now the casino has a perfect spread position. One player will collect $36,000, but with $38,000 on the table the casino has a sure profit of $2,000.
赌场不希望看到赌客在某个结果上押大额赌注，无论是轮盘还是其他赌场游戏。虽然赔率仍然对赌场有利，但如果赌注足够大，且赌客运气不错，短期的运气不佳可能会对赌场造成冲击。事实上，如果赌客知道赔率对他不利，并希望获得最大获利机会，他最好的策略是在一个结果上押最大金额，并寄希望于短期内的好运。如果他持续进行长时间的投注，概率法则最终会将他拉回现实，赌场也会最终赢得他的资金。从赌场的角度来看，理想的情况是38位玩家在轮盘上对所有38个号码各下注1000美元。这样赌场就有了一个完美的分散位置。虽然一位玩家会赢得3.6万美元，但赌场在桌面上的3.8万美元保证了其2000美元的利润。
The option trader prefers to spread for the same reason that the casino prefers the bets to be spread around the table: spreading maintains profit potential but reduces short-term risk. There is no perfect spread position for the option trader, as there is for a casino. But the intelligent option trader learns to spread off his risk in as many different ways as possible in order to minimize the effects of short-term bad luck.
期权交易者之所以喜欢分散风险，正如赌场希望赌注分散一样：分散能保持盈利潜力，但降低短期风险。期权交易者并没有赌场那样的完美分散位置。但聪明的期权交易者会尽可能多地通过各种方式来分散风险，以减少短期运气不佳的影响。
New traders are sometimes astonished at the size of the trades an experienced trader is prepared to make. For example, an independent floor trader in Treasury Bond options at the Chicago Board of Trade who buys 100 calls at 2-00 ($2,000) each has taken a position worth $200,000. How can he afford to do this? His capital resources certainly play a role in the risk he is willing to accept. But equally important is his ability to spread off risk. An experienced trader may know a wide variety of ways to spread off the risk associated with the 100 calls he purchased, either using other options, futures contracts, cash bonds, or some combination of these instruments. He may not be able to completely eliminate his risk. But he may be able to reduce it to such an extent that his risk is actually less than that of a much smaller trader who does not know how to spread, or knows only a limited number of spreading strategies.
新交易者有时会对经验丰富的交易者愿意进行的交易规模感到震惊。例如，在芝加哥商品交易所的独立国债期权交易员，买入100个期权合约，每个合约价格为2.00美元（共2000美元），相当于200,000美元的头寸。他是如何做到的呢？他的资本资源当然影响着他愿意接受的风险。但同样重要的是，他能够分散风险的能力。一位经验丰富的交易者可能掌握多种方式来分散与他购买的100个期权相关的风险，无论是使用其他期权、期货合约、现金债券，还是这些工具的某种组合。他可能无法完全消除风险，但他能够将风险降低到比那些不知道如何分散风险的小交易者还要低的程度。
No comments:
Post a Comment