Abstract:
Dupire's identity is very useful for the calibration of option pricing models. We show that it is not limited to European options based on a single Brownian driven asset. By using the adjoint equations of the financial models we extend the concept to barrier options, Lévy driven options, basket options and partially to stochastic volatility models. The technique does not work for American and Asian options. The analytic derivations of theses Dupire-like formula is tested numerically and excellent agreement is found proving henceforth that the method is also numerically feasible.
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