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Parametrix approximations for option prices

We propose the use of a classical tool in PDE theory, the 
parametrix method, to build approximate solutions to generic 
parabolic models for pricing and hedging contingent claims. We 
obtain an expansion for the price of an option using as starting 
point the classical Black&Scholes formula. The approximation can 
be truncated to any number of terms and easily computable error 
measures are available.