英文标题：
《A mixed Monte Carlo and PDE variance reduction method for foreign
exchange options under the Heston-CIR model》
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作者：
Andrei Cozma, Christoph Reisinger
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最新提交年份：
2016
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英文摘要：
In this paper, the valuation of European and path-dependent options in foreign exchange (FX) markets is considered when the currency exchange rate evolves according to the Heston model combined with the Cox-Ingersoll-Ross dynamics for the stochastic domestic and foreign short interest rates. The mixed Monte Carlo/PDE method requires that we simulate only the paths of the squared volatility and the two interest rates, while an \"inner\" Black-Scholes-type expectation is evaluated by means of a PDE. This can lead to a substantial variance reduction and complexity improvements under certain circumstances depending on the contract and the model parameters. In this work, we establish the uniform boundedness of moments of the exchange rate process and its approximation, and prove strong convergence in $L^p$ ($p\\geq1$) of the latter. Then, we carry out a variance reduction analysis and obtain accurate approximations for quantities of interest. All theoretical contributions can be extended to multi-factor short rates in a straightforward manner. Finally, we illustrate the efficiency of the method for the four-factor Heston-CIR model through a detailed quantitative assessment.
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中文摘要：
在本文中，当货币汇率按照赫斯顿模型和随机国内外短期利率的Cox-Ingersoll-Ross动力学演化时，考虑外汇市场中欧式期权和路径依赖期权的估值。混合Monte Carlo/PDE方法要求我们只模拟平方波动率和两个利率的路径，而“内部”Black-Scholes型预期通过PDE进行评估。根据合同和模型参数，在某些情况下，这可能会导致显著的方差减少和复杂性提高。在这项工作中，我们建立了汇率过程及其近似的矩的一致有界性，并证明了后者在$L^p$（$p\\geq1$）中的强收敛性。然后，我们进行方差缩减分析，获得感兴趣的数量的精确近似值。所有的理论贡献都可以直接推广到多因素短期利率。最后，我们通过详细的定量评估，说明了该方法对四因素Heston CIR模型的有效性。
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分类信息：

一级分类：Quantitative Finance 数量金融学
二级分类：Computational Finance 计算金融学
分类描述：Computational methods, including Monte Carlo, PDE, lattice and other numerical methods with applications to financial modeling
计算方法，包括蒙特卡罗，偏微分方程，格子和其他数值方法，并应用于金融建模
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