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. Presented approach also gives a new insight into the classical Black-Scholes formula. Rigorous proofs of some known results are also given.
"Option Price When the Stock is a Semimartingale." Electron. Commun. Probab. 7 79 - 83, 2002. https://doi.org/10.1214/ECP.v7-1049