Equity Volatility Skew

Equity Volatility Skew

Equity Volatility Skew, sometimes called strike skew, is the measure of the disparity of option implied volatility for option contracts with different strikes but the same expiration. It is the extrapolated tangent between two given strikes implied volatility, and thus a slope.

                                                                                        

In equities, most of the time, it has a negative slope and is expressed by moneyness as the arithmetic difference between implied volatility of the 90% put option and the implied volatility of the 110% call option. It can also be expressed by strike (sticky strike, vol by constant strikes) or by delta (sticky delta, vol by delta constant).

Source: Bloomberg

Skew and Black Scholes

Existence of Strike skew is not predicted by the Black-Scholes model. Black Scholes model assumes that volatility is a property of the underlying instrument, so the same implied volatility value should be observed across all options on the same instrument.

Equity volatility skew is a consequence of empirical violations of the black Sholes stock prices return distribution assumptions. Indeed, the Black-Scholes model assumes that stock prices are lognormally distributed, which in turn implies that stock log-prices are normally distributed.

Reasons for a Skew

Empirical: Market returns are more leptokurtic than assumed in by the lognormal distribution. Market leptokurtosis would make way out-of-the-money or way in-the-money options more expensive than would be assumed by the Black-Scholes formulation. So by increasing prices for such options (and thus implied volatility), existence of implied volatility skew is a way of achieving higher prices than within the Black-Scholes model.

Statistical: Markets tend to fall harder than they rise and skewness is a measure of the asymmetry of the distribution. Being the 3rd standardized moment and representing this asymmetry, skewness expresses in a certain way the observed correlation between the move of a random process and its volatility (on this - to assess the risk neutral distribution asymmetry implied by an option, a theoretical framework or model is needed)

Behavourial: Volatility skew could reflect investors fear of market crashes, as deeply out of the money puts are a form of insurance against market crashes. As they are considered as low cost in terms of dollars, deeply out of the money puts are widely used as a protection tools. Thus, skew can be seen as the perceived tail risk of the distribution of the market and can be a valuable indicator that shows the market sentiment toward a given underlying.

Structural Demand and Supply: The market is ‘long stock’, so investors naturally tend to sell high strike calls options (to enhance the yield of the portfolio through income) and to buy puts options in order to protect the portfolio returns.

Use of the skew:

The first thing is that there is not a single measure of equity volatility skew that is unambiguously best for all purposes. In fact, skew is dependent from volatility level, maturity, spot price. A very interesting way of expressing skew is (25 delta put volatility-25 delta call volatility) / 50 delta volatility, which emerges as the preferred skew measure based on the theoretical and empirical analysis.

Predictive power of returns: Academics tend to suggest that there is predictive information content within the volatility skew, especially in the short-term for stock market returns. However, market practitioners tend to make no money from such findings. So it seems that there is no clear empirical relationship... Sorry guys.

There have been many attempts in the academic literature to model the behavior of changes in skew, but the interpretation of skew information by traders is still done largely on a qualitative and ad hoc basis.

Trading Skew

An experienced trader explained me a rule of thumb, 10 delta difference between 2 options should roughly equate to 1 vol difference. Skew will be expensive if above 1.5 and cheap if below 0.5.

Risk Reversals, Put Spreads and Call Spreads are skew trading strategies. The main drawbacks when entering such king of strategy is that realisation of the skew will be impacted by vol level and spot level, so a decent amount of noise will come affect the trade. As the trade is done, moneyless/delta of the options is affected by the spot and/or volatility changes and passage of time.

Also, when trading short term options (less than 3m, for example) most of skew buying strategies tend to have poor gamma/theta ratios. In other words owning gamma via puts with high skews can be expensive in terms of theta decay compared to a portfolio made up of at-the-money or call options.