基于CBI时间变换Lévy过程的多货币建模
CBI-time-changed Lévy processes for multi-currency modeling
AI总结：
本文提出基于CBI时间变换Lévy过程的多货币随机波动率框架，利用仿射过程理论保证解析可处理性和风险中性测度不变性，并通过Fourier方法与深度学习校准在货币三角数据上验证了模型的有效性。
摘要：
我们基于CBI时间变换Lévy过程，开发了一个用于多货币建模的随机波动率框架。所提出的框架捕捉了外汇市场的典型风险特征，并与外汇汇率的对称性保持一致。此外，由于CBI过程的自激励行为，外汇汇率的波动率表现出自激励动态。借助仿射过程理论，我们证明了该方法在解析上是可处理的，并且模型结构在一类适当的风险中性测度下保持不变。通过Fourier方法得到了货币期权的半封闭定价公式。我们提出了两种校准方法，其中一种也依赖于深度学习技术，并证明该模型的一个简单设定能够在货币三角的市场数据上取得良好的拟合效果。
英文摘要：
We develop a stochastic volatility framework for modeling multiple currencies based on CBI-time-changed Lévy processes. The proposed framework captures the typical risk characteristics of FX markets and is coherent with the symmetries of FX rates. Moreover, due to the self-exciting behavior of CBI processes, the volatilities of FX rates exhibit self-exciting dynamics. By relying on the theory of affine processes, we show that our approach is analytically tractable and that the model structure is invariant under a suitable class of risk-neutral measures. A semi-closed pricing formula for currency options is obtained by Fourier methods. We propose two calibration methods, also by relying on deep-learning techniques, and show that a simple specification of the model can achieve a good fit to market data on a currency triangle.
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