Stability of the European Option Value Function Under Jump-Diffusion Process

Abstract

We consider a financial market where there are brusque variations in the price of an asset and an European option on this asset. In
this setup the value as well as the hedging process functions are expressed in the form of infinite series. For finite expectation of the jumps proportions, we give sufficient condition on the payoff function which leads to the convergence of the infinite series. We also obtain the upper bound for the value function, hedging portfolio process as well as for the hedging process in the Black-Sholes setup. Moreover, we use probabilistic approach to investigate the variation of the value function.