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

Yu Xing, Dingcheng Wang and Xiaoping Yang

Communications in Statistics - Theory and Methods, 2021, vol. 50, issue 5, 1059-1081

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.

Date: 2021
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DOI: 10.1080/03610926.2019.1646763

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