Equilibrium Valuation of Currency Options Under a Discontinuous Model With Co-Jumps

Abstract

In this paper, we study the equilibrium valuation for currency options in a setting of the two-country Lucas-type economy. Different from the continuous model in Bakshi and Chen [1], we propose a discontinuous model with jump processes. Empirical findings reveal that the jump components in each country's money supply can be decomposed into the simultaneous co-jump component and the country-specific jump component. Each of the jump components is modeled with a Poisson process whose jump intensity follows a mean reversion stochastic process. By solving a partial integro-differential equation (PIDE), we get a closed-form solution to the PIDE for a European call currency option. The numerical results show that the derived option pricing formula is efficient for practical use. Importantly, we find that the co-jump has a significant impact on option price and implied volatility.

Locally Risk-Minimizing Hedging for European Contingent Claims Written on Non-Tradable Assets With Common Jump Risk

“…Analogously, the common jump process is used to represent the jump triggered by systematic shocks such as financial crisis. For more discussions on the risk process with common jump, the reader can be referred to Wang [29] and Xing et al [31]. To obtain a closed-form pricing formula of a European call option, we employ the Fourier transform method to solve a partial integro-differential equation (PIDE).…”