Skewness and Kurtosis in Options
Skewness measures the asymmetry of expected return distributions priced into options markets, while kurtosis captures the probability mass in the tails; together they explain why out-of-the-money puts typically carry higher implied volatility than out-of-the-money calls in equity index options.
The Black-Scholes model assumes that asset returns are normally distributed — a symmetrical bell curve with thin tails. Empirical evidence from equity markets globally, and specifically from NSE data, consistently contradicts this assumption. Actual equity return distributions exhibit negative skewness (more extreme negative returns than positive ones of the same magnitude) and excess kurtosis (fat tails — both positive and negative extreme returns are more frequent than a normal distribution would predict).
Skewness in the context of options pricing manifests as the volatility skew. In equity index options, it is almost universally negative: out-of-the-money puts command higher implied volatility than out-of-the-money calls at the same distance from the current price. On NSE, the Nifty 50 volatility skew is persistent and deepens significantly during risk-off periods. A 5% out-of-the-money put might trade at an IV of 20% while the at-the-money option trades at 14% and a 5% out-of-the-money call at 11%. This represents the market's collective willingness to pay extra for downside protection — a direct consequence of loss aversion and institutional hedging demand.
Kurtosis, specifically excess kurtosis (kurtosis greater than 3, the value for a normal distribution), describes fat tails. Options on instruments with high kurtosis will show elevated implied volatility for deep out-of-the-money strikes on both sides relative to the at-the-money implied volatility, creating a volatility smile rather than a pure negative skew. In individual stock options, particularly for event-driven situations (corporate results, merger announcements), kurtosis can be extreme because the probability of a large gap move in either direction is non-trivial.
For risk management, skewness and kurtosis have practical implications. A delta-neutral options portfolio that assumes log-normal returns will systematically underestimate the probability of a large downward move and overestimate the premium appropriate for tail risk protection. The 2008 global financial crisis and the March 2020 Indian market crash (when Nifty fell approximately 38% in five weeks) are canonical examples of kurtosis events — outcomes that were assigned near-zero probability by normal-distribution models.
Advanced options pricing models such as the Heston stochastic volatility model, Variance Gamma model, and jump-diffusion models were developed specifically to incorporate skewness and kurtosis into option valuations. While these are primarily used by institutional desks and market makers, retail traders can proxy their effects by comparing observed implied volatility at different strikes — the shape of the volatility surface encodes the market's current assessment of skewness and kurtosis without requiring the trader to solve a partial differential equation.