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Option price when the stock is a semimartingale. (English) Zbl 1008.60057

Summary: The purpose of this note is to give a PDE satisfied by a call option when the price process is a semimartingale. The main result generalizes the PDE in the case when the stock price is a diffusion. Its proof uses Meyer-Tanaka and occupation density formulae. The presented approach also gives a new insight into the classical Black-Scholes formula. Rigorous proofs of some known results are also given.

MSC:

60G35 Signal detection and filtering (aspects of stochastic processes)
91B28 Finance etc. (MSC2000)
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