Equilibrium pricing of foreign exchange options under a discontinuous model with stochastic jump intensity

Abstract

In the setting of the two-country Lucas-type economy, we study the equilibrium valuation for foreign exchange options under a discontinuous model with stochastic jump intensity. In our model, we add a Poisson-type jump with stochastic jump intensity into the two-factor stochastic volatility process of money supply in each country. By solving a partial integro-differential equation (PIDE), we get a closed-form solution for a European call currency option. By setting different values of parameters, our model can contain some existing models as special cases. Meanwhile, the numerical results show the derived option pricing formula is efficient for practical use and the stochastic jump intensity has significant impacts on implied volatilities.

Keywords:

• Equilibrium pricing
• foreign exchange option
• partial integro-differential equation
• stochastic jump intensity

MATHEMATICS SUBJECT CLASSIFICATION:

• 60G05

Acknowledgments

The authors would like to thank anonymous reviewers who gave many valuable suggestions which are very helpful to improve the quality of the manuscript.

Additional information

Funding

A project funded by Natural Science Foundation for Youths of Jiangsu Province (BK20171072), Natural Science Foundation of the Higher Education Institutions of Jiangsu Province (17KJB110007), Open Project of Jiangsu Key Laboratory of Financial Engineering (NSK2015-15), National Natural Science Foundation of China (71871120), Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), National Natural Science Foundation of China (71501099).