Skew arbitrage: How can you realize the skewness of the underlying?

It's not clear to me how to realize skewness. In other words, how do you implement skew arbitrage? There seems to be no well-known recipe like in volatility arbitrage.

Volatility arbitrage (or vol arb) is a type of statistical arbitrage implemented by trading a delta neutral portfolio of an option and its underlier. The objective is to take advantage of differences between the implied volatility and a forecast of future realized volatility of the option's underlier.

My hypothetical skew arbitrage definition:

Skew arbitrage is a type of statistical arbitrage implemented by trading a delta and volatility neutral portfolio. The objective is to take advantage of differences between the implied skew and a forecast of future realized skew of the option's underlier.

Is it possible to make such a skew-arb portfolio in practice? If I have great confidence in my skew forecast but not in my volatility forecast, I am tempted to engage in this type arbitrage. But again, this is just a hypothetical version of skew arbitrage. If you know a correct and more practical version, you are welcome to correct me!

The same question but in a different voice: In practice, a skew bet is implemented through vertical spread, i.e. buying and selling options of different strikes. How do options traders hedge / realize the edge of the spread they trade that is indifferent to the underlying volatility?

Great question!

I think the most useful starting point is Stock Return Characteristics, Skew Laws, and the Differential Pricing of Individual Equity Options by Bakshi, Kapadia and Madan (2003). Their paper proposes a definition of model-free implied skewness (they originally called it risk-neutral skewness, but MFIS is more accurate), which they prove will have a P&L directly proportional to the realized skewness of the underlier.

Subsequent papers (there are literally dozens) have thoroughly explored the properties of MFIS. In particular, Does Risk-Neutral Skewness Predict the Cross-Section of Equity Option Portfolio Returns? by Bali and Murray (2011) estimates the empirical average returns to delta-neutral and vega-neutral skewness portfolios, and they find a strong negative relation between implied risk-neutral skewness and the returns of a skewness portfolio, consistent with a positive skewness preference.

By the way, there are two different concepts involved here. The first is options implied-volatility skew, which relates to the way volatility changes as a function of price (reflected in options as a function of strike price). The second is the skewness of the underlier, which is a property of the returns distribution. Since you talk about "realizing skew," I believe you are referring to the second concept, which is the focus of BKM (2003).

• Glad you like it and thanks for editing. I will definitely look into it, and see what I can extract and get back to everyone. Oct 3, 2011 at 21:09
• Bravo! I think your second reference is almost what I am looking for (haven't finished it yet but can feel it). Thank you, Tal. This paper is highly relevant and helpful. Oct 7, 2011 at 1:41

Skew "arbitrage" is a pretty broad term. When you are trading the skew, there are 3 principal risks (or sources of P&L, if you will):

1. The actual change in the slope of the skew in the implied space. e.g. if you are trading 95% strike against 105% strike and your underlying stays in place, all of your instantaneous P&L would be due to the changes in the implied vol at each strike times the Vega per leg

2. Realization of volatility across the strike space. that is, if the underlying drifts to one of the strikes, what would be the volatility realized along the way and how it relates to the original difference in vols that you locked in

3. The implied volatility of across the realized strike space. that is, if the underlying goes to the vicinity of one of the two strikes, what would be the implied volatility that you have to buy back or sell

In general, what you are going to trade is either going to be some sort of risk reversal/collar or a 1 by N put or call spread in a delta-neutral manner. It is, however, very hard to separate the 3 risks above from each other using vanilla structures, assuming that your underlying actually moves. You can try to play different risk factors by selecting your maturities and/or strikes.

PS. I, unfortunately, run a number of skew-related strategies, so it's going to be hard to discuss specific strategies without revealing much of my proprietary methods.

The paper "Do option markets correctly price the probabilities of movement of the underlying asset? " by Yacine Aït-Sahalia, Yubo Wang, and Francis Yared should in my opinion provide many very usefull elements for this question (look in particular at section 3).

Regards

• Thank you TheBridge. The title of this paper seems to be a better question than mine! Give me some time to digest. I will extract the ideas and merge it to this question. Oct 3, 2011 at 21:09

I just thought it is worth mentioning that the skew of the underlier implied by traded option prices and the options implied-volatility skew are indeed related by no-arb relation. The point is that you can integrate implied variance over the strike prices to get the unconditional implied variance (and hence volatility) of the underlier and the skewness of the underlier gives you the extent to which the integral is different from the integrands.

Hi this is only an "arbitrage" if your vol forecast is accurate to the dot, which is not very practical.

The closest thing to vol arb is the dispersion trade, which gets you the return in the "implied skew".