Local vs Non-local Forward Equations for Option Pricing
نویسندگان
چکیده
When the underlying asset is a continuous martingale, call option prices solve the Dupire equation, a forward parabolic PDE in the maturity and strike variables. By contrast, when the underlying asset is described by a discontinuous semimartingale, call prices solve a partial integro-differential equation (PIDE), containing a non-local integral term. We show that the two classes of equations share no common solution: a given set of option prices is either generated from a continuous martingale (”diffusion”) model or from a model with jumps, but not both. In particular, our result shows that Dupire’s inversion formula for reconstructing local volatility from option prices does not apply to option prices generated from models with jumps.
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