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.

中文翻译：

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具有共跳的不连续模型下的货币期权的均衡估值

在本文中，我们研究了两国卢卡斯型经济背景下货币期权的均衡估值。与 Bakshi 和 Chen [1] 中的连续模型不同，我们提出了一个带有跳跃过程的不连续模型。实证结果表明，每个国家货币供应量的跳跃成分可以分解为同时的共同跳跃成分和特定国家的跳跃成分。每个跳跃分量都用泊松过程建模，其跳跃强度遵循均值回归随机过程。通过求解偏积分微分方程 (PIDE)，我们得到了欧式看涨货币期权 PIDE 的封闭式解。数值结果表明，导出的期权定价公式在实际应用中是有效的。重要的，