Markov-Modulated Jump-Diffusions for Currency Option Pricing

17 Pages Posted: 10 Apr 2011

See all articles by Xuewei Yang

Xuewei Yang

Nanjing University - School of Management and Engineering; Nanjing University - Institute of New Finance

Yongjin Wang

Nankai University - Business School

Lijun Bo

University of Science and Technology of China (USTC)

Date Written: January 16, 2010

Abstract

This article introduces dynamic models for the spot foreign exchange rate with capturing both the rare events and the time-inhomogeneity in the fluctuating currency market. For the rare events, we use a compound Poisson process with log-normal jump amplitude to describe the jumps. As for the time-inhomogeneity in the market dynamics, we particularly stress the strong dependence of the domestic/foreign interest rates, the appreciation rate and the volatility of the foreign currency on the time-varying sovereign ratings in the currency market. The time-varying ratings are formulated by a continuous-time finite-state Markov chain. Based on such a spot foreign exchange rate dynamics, we then study the pricing of some currency options. Here we will adopt a so-called regime-switching Esscher transform to identify a risk-neutral martingale measure. By determining the regime-switching Esscher parameters we then get an integral expression on the prices of European-style currency options. Finally, numerical illustrations are given.

Keywords: Spot Foreign Exchange Rate, Rare Event, Time-Inhomogeneity, Esscher Transform, Currency Option

JEL Classification: C13, C15, F31

Suggested Citation

Yang, Xuewei and Wang, Yongjin and Bo, Lijun, Markov-Modulated Jump-Diffusions for Currency Option Pricing (January 16, 2010). Insurance: Mathematics and Economics, Forthcoming, Available at SSRN: https://ssrn.com/abstract=1368785

Xuewei Yang (Contact Author)

Nanjing University - School of Management and Engineering ( email )

22 Hankou Road, Gulou District
Nanjing, Jiangsu 210093
China

Nanjing University - Institute of New Finance ( email )

Nanjing, Jiangsu 210093
China

Yongjin Wang

Nankai University - Business School ( email )

94 Weijin Road, Nankai District
Tianjin, 300071
China

Lijun Bo

University of Science and Technology of China (USTC) ( email )

96, Jinzhai Road
Hefei, Anhui 230026
China