Pricing options on securities with discontinuous returns

Abstract

We consider a financial market where the asset prices are driven by a multidimensional Brownian motion processs and a multidimensional point process of random jumps admitting stochastic intensity. Using the equivalent martingale measure approach, we construct hedging portfolios for European and American contingent claims. We also present a valuation equation that must be satisfied by any derivative security and can be solved numerically to obtain option prices.