Stochastic volatility refers to models in which the volatility of an underlying asset is itself a random process, evolving over time according to its own stochastic dynamics rather than being constant or a fixed function of price and time. The most widely used stochastic volatility model is the Heston model, which assumes volatility follows a mean-reverting square-root process correlated with the asset's price process. Stochastic volatility models better capture real-world phenomena like volatility clustering, fat tails, and the volatility skew observed in Nifty 50 and Bank Nifty options markets. They are essential for pricing path-dependent and exotic options accurately. The key parameters — mean reversion speed, long-run variance, volatility of volatility, and correlation — are calibrated to the observed implied volatility surface in Indian options markets.
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