译者 王为
文中黑字部分为原文，蓝字部分为译文，红字部分为译者注释或补充说明The Rationale for Ag Options’ Upward Skew
By Erik Norland
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Across most markets, out-of-the-money (OTM) put options tend to be more expensive than OTM call options. This is most obviously true in the equity market, where investors fear downside risks more than upside risks. It’s also true in the crude oil market, where, despite political risks to the upside, downside risk is usually the main concern. Precious metals, fixed income and currency markets are quirkier and, by-and-large, upside and downside risks are more symmetrical or, at least, more time varying. Options on agricultural goods, however, are unique: call options are usually more expensive than puts – between 74% and 99% of the time since early 2017, depending on the product (Figures 1 -3).
大多数市场的价外看跌期权的期权费往往高于价外看涨期权的期权费，这一点在股票市场上尤其明显，因为投资者担心的是股市下跌而不是上涨。原油市场也是如此，尽管政治风险会导致油价走高，但市场通常最担心的是油价的下跌。贵金属、固定收益和外汇市场的情况更特殊一些，总的来看，在这些市场中行情上涨和下跌的概率更均衡一些，至少会更加因时而动。但是，农产品期权市场却独具风格：根据具体品种的不同，在2007年初至今74%至99%的时间里，各类农产品看涨期权的期权费通常比看跌期权更贵，见图1-3。
[h2]Figure 1: Since 2007, Corn Options Have Been Positively Skewed 84% of the Time; Wheat 99%.[/h2]2007年以来，玉米期权的波动率在84%的时间里呈现正偏斜状态，而小麦期权的波动率在99%的时间里体现为正偏斜
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[h2]Figure 2: Soybean & Soymeal Have Been Positively Skewed 74% & 80% of the Time, Respectively.[/h2]同一时期，大豆和豆粕期权的波动率分别在74%和80%的时间里处于正偏斜状态
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There are two broad explanations for the upside skew (also called “risk reversal”) in ag options. First, it could be that the underlying price behavior in these markets shows positive skewness. If so, the positive skewness in options markets would be a logical response. Secondly, if there is no positive skewness in underlying prices returns, the other major explanation is market structure: food buyers are more willing to pay premiums for upside protection than farmers are to pay for downside protection.
对于农产品期权波动率的向上偏斜现象（期权波动率偏斜也被称为“风险逆转”）有两个常见的解读。一是由于作为标的物的农产品品种的价格回报率呈现向上偏斜状态。果真如此的话，期权市场的正偏斜现象就应该符合逻辑了；其次，如果农产品的价格回报率并没有呈现正偏斜，另一种解释就认为这与市场结构有关，食品的买家更愿意支付溢价以防范食品价格的上涨而不是价格的下跌。
[h2]Figure 3: Since January 2007, Soybean Oil Options Have Been Positively Skewed 99.3% of the Time.[/h2]2007年一月份以来，豆油期权的波动率在99.3%的时间里为正偏斜![]()
The first of these explanations is easy to test. While one might imagine that the threat of droughts, floods, heat waves and cold spells might put a positive skew in agricultural goods price returns, using daily data since 1970, there is no persistent upside skewness to the underlying returns of corn, wheat, soybeans or soymeal. In fact, soybeans have shown a persistent, if slight, negative skewness in daily price returns. Soybean oil is an exception. Since 1970, there has been a slight upside skewness in daily price returns but not one that would pass most significance thresholds: usually skewness has to be greater than +0.5 to meet even minimal significance tests (Figure 4).
对第一个解读很容易就可以做一下测试。有人可能会认为干旱、水涝、热浪和寒流等风险会导致农产品价格的回报率呈现正偏斜状态，但如果对1970年代以来的每日价格数据进行分析就会发现，玉米、小麦、大豆或豆粕价格的回报率并没有体现出明显的正偏斜。实际上，大豆每日价格的回报率有一些持续的负偏斜，虽然程度并不大。豆油是个例外，1970年以来，豆油每日价格的回报率只是略微向上偏斜，但是偏斜程度并没有超过具有统计学上的显著性意义所需要的门槛，通常偏斜程度需不低于+0.5才能通过统计学上的显著性测试，见图四。
[h2]Figure 4: Outside of Soybean Oil, there is no Persistent Upside Skewness in Daily Price Returns.[/h2]除了豆油，其他农产品的每日价格回报率并没有展现出持续的向上偏斜特点
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As such, this leaves us with the structural explanation of the upside skewness in crop options markets. On the supply-side of the agricultural markets are millions of farms operating world-wide, including 2.16 million in the US alone. For these millions of farmers, the chief risk is, of course, a decline in prices. On the demand side are a relatively small number of firms that purchase a large portion of the world’s crops for processing, distribution and sale. For these food buyers the primary risk in a sudden and extreme rise in prices.
这样的话，关于农产品期权波动率向上偏斜现象的解读就是与市场结构有关了。在农产品市场的供给侧，全球有数以百万计的农户正在经营，仅美国本土就有216万。对于这数百万农户来说，最主要的风险当然是农产品价格的下跌。在农产品市场的需求侧，数量相对有限的一些企业买走了全球谷物产量中的绝大部分用于加工、配送和向下游销售。对这些食品买家来说，最主要的风险在于农产品价格突然和极端地上涨。
The upside skewness may result from a combination of factors. First, many producers may sell their grains and oilseeds forward but then buy call options so that they can benefit from extreme upside moves in prices. While hedging strategies vary from producer to producer, they may in aggregate be more willing to sell futures and buy calls than to hedge by buying put options. Secondly, buyers of grains and oilseeds, who are much less numerous, may be willing to hedge extreme upside risk with OTM calls. This isn’t to suggest that there aren’t food producers or even food buyers who use puts; rather that there is a structural bias in the market for paying for more for OTM calls than paying for OTM puts despite a general lack of evidence that agricultural goods markets are more susceptible to extreme upside than extreme downside moves.
农产品期权波动率的正偏斜现象有可能是多个因素共同作用的结果。首先，很多谷物和油料种子的生产者会在收获前提前卖出相应的期货合约，随后会买入其看涨期权，这样就可以从价格的极端上涨行情中受益。虽然各个生产者的对冲策略各不相同，但作为整体他们可能更愿意卖出农产品的期货合约并买入看涨期权，而不是用买入看跌期权的方法对冲农产品的价格下跌风险。其次，谷物和油料种子的买家，从数量上看会非常少，可能愿意用价外看涨期权对冲农产品价格的极端上涨行情。这并不是说食品生产商甚至是食品的买家不会买入看跌期权，而是说市场上存在结构性的因素导致客户更倾向于为价外看涨期权而不是价外看跌期权支付高价，尽管并没有足够的证据显示农产品市场对价格的极端上涨而不是价格的极端下跌更敏感。
The other item to note about skewness is that it isn’t consistent over time. Sometimes the agricultural goods markets do show negative skewness. Is this a warning sign of further price declines to come? Or is it a signal that agricultural goods are oversold and that prices are likely to bounce back? Likewise, at times the upwards skewness moves to extreme levels. Is this a signal of further prices rises to come or a signal that the market is overbought and susceptible to near term declines? Our analysis doesn’t provide a definitive answer to these questions but might nevertheless offer some useful insights.
还有一个值得注意的地方是期权波动率的偏斜程度会随着时间的推移而发生变化，有时候农产品市场确实出现过期权波动率的偏斜形态为负的情况。这预示着未来的价格将往下走？抑或预示着该类农产品已处于超卖状态，价格有可能出现反弹？同样在某些情况下，期权波动率的正偏斜形态会达到极端高的程度。这是否预示着未来的价格将上涨？抑或预示着该市场已经超买并有可能在近期出现价格下跌的情况？虽然我们的分析并没有对这些问题给出明确的答案，但不管怎么说还是有可能为找出这些问题的答案给予一些有用的启示。
To answer these questions, we indexed the skewness on a scale of 0-100 over rolling two-year periods and compared it to the actual payoff of a fully funded long futures position in the various crops over the subsequent three months (so there’s no look-ahead bias). For example, if the crop option skewness was the most skewed to the downside it had been during the previous two years, the index would have a reading of zero. If the crop option market was the most positively skewed that it had been during the past two years, the index would have a reading of 100. We then broke the results down into deciles and looked at the subsequent three-month performance of the reinvested futures rolled 10 days prior to expiry from 2008 until early 2019.
为回答这些问题，我们将每两年的期权波动率的偏斜程度用0-100的数值予以表示，并将该数值与随后三个月各类农产品的不带任何杠杆的期货合约做多头寸的实际回报率进行对比，这样就不会有偏差。举个例子，如果在过去两年里谷物期权的波动率向下偏斜的程度达到极端值，那么该指数的读数为0；如果在过去两年里谷物期权的波动率向上偏斜的程度达到极端值，那么该指数的读数为100。然后我们将统计结果分成十个档，观察一下在2008年至2019年初期间滞后期为三个月的期货合约到期前十天滚动再投资的回报表现。
In the two markets which have the strongest tendency to be positively skewed, soybean oil and wheat, options traders did a pretty good job of anticipating directional risks between 2008 and 2019. When upside skewness was less than average (and in rare cases outright negative), futures prices tended to fall over the next three months. When skewness was exceptionally positive, the return on futures contracts tended to be more positive (Figure 5 and 6).
期权波动率最容易出现正偏斜状态的豆油和小麦期权市场里，交易员在2008年至2019年期间卓有成效地预测了未来价格的走势。在期权波动率的正偏斜程度低于历史均值（在极端情况下甚至进入负值区域）的时候，随后三个月的豆油和小麦期货合约的价格往往出现下跌；在期权波动率的正偏斜程度处于极端正值的时候，豆油和小麦期货合约的价格回报率往往是正的，见图5和图6。
[h2]Figure 5: Soybean Oil Options Skewness Has Been Positively Correlated with Future Price Movements.[/h2]豆油期权波动率的偏斜程度与豆油未来价格的走势正相关
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[h2]Figure 6: Lower-Than-Average Positive Skewness in Wheat has Often Signaled Further Price Declines.[/h2]小麦期权波动率的正偏斜程度低于历史均值经常会预示着小麦价格会进一步下行
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For soybeans and soymeal, the two options markets with the weakest inclination towards positive skewness in options prices, the correlation between the degree of skewness and subsequent movements in futures prices has worked the opposite way. Extreme positive skewness was often a sell signal during the 2008 to 2019 period whereas extreme negative skewness sometimes signaled those markets hitting bottom and were about to rally (Figures 7 and 8).
对于大豆和豆粕来说，这两类期权价格趋向正偏斜的可能性最小，期权波动率偏斜程度和所对应的期货合约价格的未来波动的相关度之间是负的。在2008-2019年期间，如果这两类商品的期权波动率的正偏斜程度达到极端水平，通常被视为卖出信号；而这两类商品的期权波动率的负偏斜程度进入极端区域，有时会预示着这两个品种的行情即将触底并将出现反弹，见图7和8。
[h2]Figure 7: Extreme Positive Skewness Sometimes Correlated with Coming Soybean Price Declines.[/h2]大豆期权波动率的极端正偏斜状态有时候与大豆价格的下跌相关联
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[h2]Figure 8: Soymeal Future Returns Correlated Negative With Its Degree of Skewness From 2008-2019.[/h2]在2008-2019年期间，豆粕期货合约与豆粕期权波动率的偏斜程度之间的相关性是负的
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Between 2008 and 2019, corn prices have done best at the extremes; when skewness was exceptionally high or low. By contrast, corn prices tended to fall over our sample period when skewness was close to its two-year moving average (Figure 9).
在2008-2019年期间，当玉米期权的波动率偏斜程度处于极端正值或负值区域之时，玉米价格的回报率往往表现得最佳。与此相反的是，同一时期当玉米期权的波动率偏斜程度接近两年移动平均水平时，玉米价格往往会出现下跌，见图9。
[h2]Figure 9: Corn Showed the Weakest Correlation with Options Skewness Among the Crops.[/h2]在各类农产品中玉米价格与玉米期权波动率的偏斜程度关联度最低
We would emphasize that these results are sensitive to their sample period and going forward the relationship between current levels of options skewness and subsequent changes in futures prices could look very different than it did in the past decade. Also, the lack of consistent result among the various agricultural goods suggests that options skewness as an indicator of future returns should be taken with a large grain of salt. Nevertheless, even for those who don’t deal in the options markets, the relative prices of OTM calls and OTM puts might be worth looking at if only to ask questions about how the market is currently positioned.
要强调的是，以上这些观察到的结果受统计期间的选择影响很大，未来，期权波动率的偏斜程度和期货合约价格的后续走势之间的关系有可能与过去十年的情况大为不同。此外，各类农产品价格的回报率缺乏持续的有效验证也说明在将期权波动率的偏斜程度作为预测农产品期货价格走势的晴雨表方面应持谨慎态度。但不管怎样，即使对于那些不在期权市场做交易的人来说，哪怕只是了解一下当前市场头寸的摆布情况，也应对价外看涨期权和价外看跌期权的期权费之间的涨跌变化给予一些关注。
[h1]Bottom Line[/h1]要点
- Agricultural options markets display a nearly consistent upward skewness.
农产品期权市场近乎一致地展现出波动率正偏斜现象
- The skewness appears to result from market structure and not from skewness in the price returns of the underlying goods.
农产品期权波动率的偏斜现象似乎是市场结构造成的，而与作为标的物的农产品品种的价格回报率的偏斜情况无关
- Wheat and soybean oil have the strongest tendency towards positive skew.
小麦和豆油期权最容易出现波动率正偏斜现象
- The degree of skewness isn’t necessarily a reliable indicator of future price movements.
- 期权波动率的偏斜程度并不一定是预测农产品期货合约价格走势的可靠指标
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