Local Volatility

Local Volatility is a model-based approach that calculates a unique, state-dependent volatility for every point on the volatility surface. Unlike constant volatility models, which assume volatility is the same everywhere, local volatility recognizes that market participants price options differently based on their current price and time to maturity.

It is derived from the observed market prices of European options and is used to price more complex exotic derivatives. By using a local volatility surface, traders can more accurately model the probability distribution of future asset prices.

This is critical for pricing path-dependent options where the payoff depends on the price history. It is a more sophisticated framework than the standard Black-Scholes model because it captures the empirical reality of the volatility smile.

However, it requires significant computational power and accurate market data to calibrate. It is a fundamental tool for quantitative desks in both traditional and crypto finance.