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

EXPLAINING OPEX DRIFT

by Kevin Muir

This post will be a little more technical, but it's important, so I urge you to read on.

这篇文章的专业难度有点高，但内容很重要，所以建议各位还是耐心看下去。

Over the past couple of years there has been an increased interest in dealers' gamma charts to help explain market movements. Strategists such as Nomura's Charlie McElligott and Marko Kolanovic from JP Morgan have been elevated to god-like status on their analysis of this somewhat complicated concept.

在过去几年里市场对交易员期权仓位的伽马值变动情况的愈发关注有助于解释美国股市为啥会发生波动，野村证券的分析师Charlie McElligott和摩根大通银行的分析师Marko Kolanovic因对这个有点复杂的概念有一些研究成果而被抬到了神一样的位置上。

在期权的各项定价要素中，德尔塔指的是期权费相对于标的资产价格的变动，比如标准普尔500指数的合约价每上涨1%，标准普尔500指数看涨期权的期权费就上涨0.5%，说明这个标准普尔500指数看涨期权的德尔塔值为0.50。但期权的德尔塔值的变动并非线性的，而伽马衡量的是标的资产价格每发生一个单位的变动，期权的德尔塔值相应的变动速度，因此期权的伽马值是期权的德尔塔值的二阶导数。如果标准普尔500指数看涨期权的伽马值为0.02，意味着标准普尔500指数的合约价每上涨1%，标准普尔500指数看涨期权的期权费就上涨0.5%+0.02%=0.52%。

My background is originally an institutional equity index trader, so although I enjoyed reading their reports to find the periods when dealers were either choking on soul-destroying quiet-market long gamma positions or scrambling with middle-of-the-night-vietnam-ambush war like short gamma positions, it wasn't immediately obvious how to use this in my trading. Yeah, sure I knew dealer positioning would dampen volatility when they were long gamma and exacerbate moves when they were short volatility, but to a large extent, the dealers were long gamma higher, and short gamma lower, so that seemed like a natural reaction. Markets go up an escalator, down the elevator. Surely, the prediction that higher markets will be more subdued and lower markets will experience higher volatility hardly seemed enlightening.

我原先是负责机构类客户的股票指数交易员，因此尽管我经常从研究机构的报告中看到交易员们要么在行情平静得无聊的时候一窝蜂地做多期权仓位的伽马值，要么像在越南战场的暗夜里遭遇了一场丛林伏击战一样争先恐后地做空伽马值的头寸，但我无法在交易中直接应用这些经验教训。我很清楚的是，如果做多期权的伽马值那么标的资产的波动率会因此而降低，而做空期权的伽马值会加剧标的资产的价格波动，但在很大程度上，交易员是在伽马值高的时候做多，伽马值低的时候做空，因此这似乎是个很自然的反应。标的资产的价格涨的时候像坐扶梯一样慢慢往上走，跌的时候却垂直掉下来。显然，那种认为价格上涨过后波动率将回落而价格下跌后波动率将回升的观点似乎并不准确。

And it's a shame I didn't dig into the concept a little deeper. The other day my podcast partner Patrick Ceresna and I were privileged to have Brent Kochuba from SpotGamma.comon the show (listen to the whole episode here - Market Huddle ). He presented me with a chart that - once I saw it - instantly made me regret not working harder on the idea that dealer positioning is affecting the market.

惭愧的是我没有对这个概念做进一步深挖。前几天，我的播客合作伙伴Patrick 和我Ceresna有幸请到 SpotGamma.com网站的博主Brent Kochuba一起做节目，一看到他展示出来的下面这张图，我就立即意识到自己对交易员持仓情况会影响行情走势这件事没有做好功课。

There are a bunch of implications from this chart. Instead of trying to tackle them all at once, I will divide them into a few posts so that I can explain each portion more thoroughly.

上图涉及到好几个方面的问题。我不准备在本文中把所有的问题一次性地全讲一遍，而是打算分批分期地进行解读，这样就可以把每一个问题都说得更透彻一些。

I want to take a moment to speculate why this dealer gamma analysis has become more important. Back in my day, when I hedged my options book, I barely dented the market. We were just one small player in a larger diverse marketplace. Nowadays, option strategies have become so popular that it's a case of the tail wagging the dog.

先花点时间说说为什么对交易员期权仓位的伽马值变动情况所做的这个分析会变得很重要。回想我当年做交易员那会儿，当我对期权持仓风险进行对冲的时候，几乎很少对市场走势产生大的影响。我所在的银行只是一个大而多元化的市场中的一个小玩家而已。而今，期权交易策略的应用变得如此广泛以至于现在已经“不是狗摇尾巴，而是尾巴摇狗了”（意指期权交易本身反过来对标的资产的价格走势产生了巨大影响）。

Whether this is result of low real rates forcing institutional investors into yield-chasing-strategies or whether it is the natural outcome of more sophisticated market participants, I am not sure. Regardless, the important thing to realize is that the preponderance of these option strategies is moving the markets in different way than previous decades. And it's important to try to understand in what way.

我拿不准这是不是由于实际利率水平的持续低迷迫使机构投资者采取了追逐高收益率的交易策略抑或更高端的市场参与者入市所带来的必然结果。不管怎样，重要的是要认识到与几十年前相比，如今这些期权交易策略一时无两的势头正在主导市场的走势。最重要的是应试着这么去看问题。

OpEx Drift

期权合约到期前，期货合约的报价会出现明显的跃升

For those who aren't aware, OpEx stands for Option Expiry. Over the past few years, there has been a pronounced tendency for markets to rise in the week in front of a big expiry (typically the quarterly quad witching dates).

给非专业人士解释一下，OpEx这个术语指的是期权的到期日。在过去几年里，美股的价格在关键的期权到期日到来前的一周里明显会倾向于上涨，最典型的例子就是每季度末的四巫日（四巫日指的是每年三月、六月、九月和十二月的第三个星期五，在这一天，股票指数期货、股票指数期权、单只股票的期权和单只股票的期货将同时到期）。

Why is that? I couldn't really confidently explain it until Brent from SpotGamma spelled it out in a language that my option-trader-brain could understand.

为啥会这样？我没有十足的把握对此做出合理的解释，直到SpotGamma.com网站的博主Brent用我这样专业的期权交易员才能明白的语言把这事说清楚了。

In most environments, the way the dealers' books are setup means that the theta decay results in a short covering of hedges.

在大多数的情况下，交易员期权仓位的时间价值的衰减将导致以对冲风险为目的的期权空头仓位被回补。

Let's make up some theoretical positions to get a sense of how this works.

下面举例说明。

Typically, clients buy out-of-the-money put protection and fund that by selling out-of-the-money calls. Obviously that's not 100% of the trades, but on the whole, that's the way most dealer books set up.

通常，客户会买入价外看跌期权以防范标的资产价格的下跌风险，但买期权是要花期权费的，为了减少因此增加的成本，交易员会在买入价外看跌期权的同时卖出价外看涨期权。显然，不是所有的交易都是这么做的，但总体看大多数交易员的期权交易头寸都是这么构成的。

So let's go through the option math of that position. I have chosen February's expiry and used 9% vol on the long call position and 12.5% vol on the short put position. Nothing changes between the two days except there is one less day in the calculations of the hedging deltas. What happens to the dealer's book between those two days?

看一下这个期权头寸是咋估值的。假设一个交易员持仓标准普尔500指数期货合约作为基础资产，为了对冲下跌风险，该交易员买入波动率为9%的标准普尔500指数看涨期权，卖出波动率为12.5%的看跌期权，这两个期权合约均将于2020年2月到期。在计算期权头寸的德尔塔值时，假设期权的估值日比交易日晚一天，在这两天里标准普尔500指数没有发生任何波动。在此情况下，该交易员的期权头寸会如何变化？

原文中的计算有误，但不影响最终的结论，我的计算过程如下：

计算结果显示，交易员在交易日需要做空价值约为12亿美元的标准普尔500指数期权合约，到了第二天也就是估值日，只需做空价值约为11.75亿美元的期权合约即可，因此该交易员需买回价值2726万美元的期货合约。

根据我的计算，交易员在交易日需要做空价值约为2.13亿美元的标准普尔500指数期货合约，到了第二天也就是估值日，只需做空价值约为2.08亿美元的期货合约即可，因此该交易员需买回价值535万美元的标准普尔500指数期货合约。

If you have ever wondered why we tend to rally on OpEx week - here is your answer. This tendency only gets more pronounced in the final days of expiry and the decay of the needed-hedges accelerates.

如果想知道标准普尔500指数的报价为啥往往会在期权到期日前的一周里出现上涨，这就是答案。这个趋势只是在期权到期前的最后几个交易日里以及以对冲风险为目的而持仓的期权的时间价值加速衰减的情况下才变得相当明显。

因为在期权到期日，期权的时间价值会变成零，因此在期权合约即将到期的时候，期权仓位的时间价值会加速衰减。

Remember last Thursday and Friday? Both days saw end of the day spikes higher.

还记得上周四1月16日和上周五1月17日吗？标准普尔500指数期货的报价在这两天里均大幅上扬，如下面两张图所示。

注意：2020年1月份交割的标准普尔500指数期权合约在1月17日即到期。

Do I think these spikes were solely the result of option hedging by dealers? Not a chance. Passive flows are often benched to the close so that is a contributing factor. But option expiry weeks are typically stronger than other weeks (with the next week being often showing weakness), and this option math shows why this is the case.

Don't underestimate the upward pull of the dealers' option book. All you need to do is look at Brent's chart:

不要低估交易员的期权仓位对股价所起到的拉动作用，只需看看下面这张来自Brent的图就知道了：

Look closely at the blue curve. The center is not at zero. Its mean is positive. And yes, I know that it might be self-fulfilling (quiet rising markets result in positive returns), but then again, maybe the option market is driving these tendencies more than some participants realize. I certainly used to be counted in that camp. Not anymore!

仔细看看蓝色曲线代表的区域，该区域的中心并没有在0这个位置上，其均值为正（如果是正态分布的话，收益率分布曲线以0为中心，左右对称）。我知道这种现象有可能意味着自我应验，也就是说股市越持续上涨，股市回报率为正的概率越大。但是话说回来，期权市场对股市回报表现的影响也许远超一些市场人士的想象。我以前当然也属于那种人，但 现在再也不是了！

In future posts I will examine other trading implications about this data. In the mean time, remember last week's rise might have more to do with dealer option hedging rather than fundamental developments. The everything-is-awesome-with-the-world crowd might be missing this possibility.

在以后的博文中，我会继续就这个专题写下去。与此同时，请记住美股大上周的上涨可能不是来自于经济基本面的驱动，而是与交易员对期权对冲头寸的调整有很大关系，那些认为“全球一切都OK”的人很可能没有看到这一点。