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).
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.
