The legacy of Dupire

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The story is well known. Traditional Black-Scholes theory takes as its dependent variable the price of an option of fixed strike and maturity, and leads to a partial differential equation where the independent variables are the underlying asset price and time. Searching for a deterministic volatility process that fitted observed market smiles, Dupire discovered a new equation for the option price – the Dupire equation – with strike and maturity as independent variables, and with time and asset p

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