Foreign equity option pricing under stochastic volatility model with double jumps

• Published in: Economic modelling Vol. 28; no. 4; pp. 1857 - 1863
• Main Authors: Xu, Weidong, Wu, Chongfeng, Li, Hongyi
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier B.V 01.07.2011; Elsevier; Elsevier Science Ltd
• Series: Economic Modelling
• Subjects: Affine jump-diffusion process; Assets; Currency; Devisenoption; Economic models; Empirical research; Equity; Exchange rate; Exchange rates; Foreign equity option; Foreign equity option Affine jump-diffusion process Fourier transformation Exchange rate; Foreign exchange rates; Fourier transformation; International finance; Optionspreistheorie; Prices; Rates of return; Securities prices; Studies; Transformation; Volatility; Foreign equity option; Fourier transformation; Affine jump-diffusion process; Exchange rate
• ISSN: 0264-9993; 1873-6122
• DOI: 10.1016/j.econmod.2011.03.016

This paper considers the challenging problem advocated by Huang and Hung (2005), that is to incorporate the stochastic volatility into the foreign equity option pricing. Foreign equity options (quanto options) are contingent claims where the payoff is determined by an equity in one currency but the actual payoff is done in another currency. Huang and Hung (2005) priced foreign equity options under the Lévy processes. In Huang and Hung's paper, they considered jumps in the foreign asset prices and exchange rates and assumed the volatility as constant. However, many studies showed that constant volatility and jumps in returns are incapable of fully capturing the empirical features of equity returns or option prices. In this paper, the stochastic volatility with simultaneous jumps in prices and volatility is proposed to model foreign asset prices and exchange rates. The foreign equity option pricing formula is given by using the Fourier inverse transformation. The numerical results show that the use of stochastic volatility with simultaneous jumps in prices and volatility proposed to model foreign asset prices and exchange rates is necessary and this approach can help us to capture more accurately the foreign equity option prices. ► This paper considers the challenging problem advocated by Huang and Hung (2005). ► We incorporate the stochastic volatility into the foreign equity option pricing. ► The foreign equity option pricing formula is given by using the Fourier inverse transformation. ► The numerical results show that our model can help us to capture more accurately the foreign equity option prices.