Foreign equity option pricing under bivariate time-varying coefficient jump-diffusion model

Abstract

This paper is dedicated to the study of the foreign equity option pricing under bivariate time-varying coefficient jump-diffusion model. Economic variables are not carved on tablets of stone, they change over time. Hence we allow the returns and variance of the equity price and foreign exchange rate are time-varying functions. Foreign equity options (quanto options) have become more and more popular in international financial markets, where the payoff depending on the equity price in one currency but the actual payoff is done in another currency. In this paper, we use a bivariate Bernoulli distribution and a bivariate Laplace distribution to model the jump indicators and jump sizes, respectively. The distribution of return is analysed by the Itô formula and normal asymmetric Laplace distribution. The pricing formula of foreign equity call option is proposed which is based on domestic currency under the risk-neutral measure. The numerical results show that the jump correlation is significant to the foreign equity option prices.