Local volatility is a model of asset price behaviour where the volatility of the underlying is assumed to be a deterministic function of both the current asset price and time, rather than a constant as assumed in the Black-Scholes model. The local volatility model, developed by Bruno Dupire, is constructed directly from observed market option prices — specifically by deriving a unique volatility surface that is consistent with all traded option prices simultaneously. For Indian options traders, local volatility models are used to price and hedge exotic options like barrier options and Asian options in a way that is consistent with the observable Nifty 50 or Bank Nifty implied volatility surface. Unlike stochastic volatility models, local volatility assumes no randomness in the volatility process itself — only in the price path.
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