Study on European put option pricing with underlying asset zero-coupon bond and interest rate following the Vasicek model with jump

Abstract

This paper examines the price of European put options with underlying asset zero-coupon bond and the interest rate that satisfied the Vasicek model with jump. The study was conducted by reconstructing the European put option pricing equation. The jump size is defined following a mixed-exponential distribution. By utilizing infinitesimal generator and martingale concepts, Laplace transform is constructed for the distribution of the Vasicek model with jump. Then, using the results of the Laplace transform for the distribution of the Vasicek model with jump and the concept of equivalent martingale measure, the European put option pricing equation with underlying asset zero-coupon bond is constructed.