Local volatility

A local volatility model, in mathematical finance and financial engineering, is one that treats volatility as a function of both the current asset level ${\displaystyle S_{t}}$ and of time ${\displaystyle t}$. As such, a local volatility model is a generalisation of the Black-Scholes model, where the volatility is a constant (i.e. a trivial function of ${\displaystyle S_{t}}$ and ${\displaystyle t}$).

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