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Hard · Options & Greeks · Quant Trader interview question · stochastic-volatility, local-volatility, options, volatility-surface
Consider two popular approaches for modeling the volatility surface: local volatility and stochastic volatility models. Local volatility models aim to capture the implied volatility surface by making volatility a deterministic function of the underlying asset price and time, $ \sigma(S_t, t) $. Stochastic volatility models, on the other hand, introduce one or more additional stochastic factors (typically volatility itself) to drive the evolution of asset prices. A common example is the Heston mo