ON PRICING EUROPEAN CALL OPTION 0N EXPONENTIAL L\'{E}VY MODEL WITH JUMPS IN INTEREST RATE

Abstract

This article presents a simple but efficient method for pricing European call option in exponential Levy model when the interest rate is stochastic with jumps. We relax two assumptions in the Black and Scholes model: geometric Brownian motion for asset price and constant interest. The asset price is assumed to be given by a more general stochastic process, the Levy process, and the interest rate in the market has stochastic paths with jumps. The resulting partial-integro differential equation(PIDE) for the option price is reduced to a system of first order partial differential equation, which is easier to solve. Hence, the option price and its sensitivities are easily obtained. AMS Subject Classification: 60G51, 60J75, 91G20