VALUATION OF VULNERABLE OPTIONS UNDER THE DOUBLE EXPONENTIAL JUMP MODEL WITH STOCHASTIC VOLATILITY

Abstract

In this paper, we extend the framework of Klein [15] [Journal of Banking & Finance 20: 1211–1229] to a general model under the double exponential jump model with stochastic volatility on the underlying asset and the assets of the counterparty. Firstly, we derive the closed-form characteristic functions for this dynamic. Using the Fourier-cosine expansion technique, we get numerical solutions for vulnerable European put options based on the characteristic functions. The inverse fast Fourier transform method provides a fast numerical algorithm for the twice-exercisable vulnerable Bermuda put options. By virtue of the modified Geske and Johnson method, we obtain an approximate pricing formula of vulnerable American put options. Numerical simulations are made for investigating the impact of stochastic volatility on vulnerable options.