Option Pricing with Jumps

Abstract

This paper discusses European option pricing under various discontinuous conditions: option and underlying prices as well as volatility and drift coefficients experience breaks. We consider vanilla and double-barrier options under double-exponential jump diffusion model with jump drift and jump volatility. Our approach consists in applying Laplace transform directly to the pricing equation with further computing option prices and risk parameters via numerical inversion of their Laplace transforms. We focus on simple close-form and quasi-close-form solutions.

Keywords: jump-diffusion, regime switching, Laplace transfrom, Barrier options

JEL Classification: C00,G00