伴随微分算法快速相关希腊文

Luca Capriotti, M. Giles
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引用次数: 37

摘要

我们展示了伴随算法微分(AAD)如何允许通过蒙特卡罗模拟计算期权价格的相关风险的极其有效的计算。构造中的一个关键点是使用分形来同时实现计算效率和准确的置信区间。我们举例说明了一种基于copula的蒙特卡罗计算一篮子标的资产上的债权的方法,并对投资组合默认期权进行了数值测试。对于投资组合中任意数量的标的资产或名称,期权价格相对于所有成对相关性的敏感性以计算成本获得,该计算成本最多为计算期权价值本身成本的4倍。对于典型的应用程序,这将导致相对于标准方法的几个数量级的计算节省。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Fast Correlation Greeks by Adjoint Algorithmic Differentiation
We show how Adjoint Algorithmic Differentiation (AAD) allows an extremely efficient calculation of correlation Risk of option prices computed with Monte Carlo simulations. A key point in the construction is the use of binning to simultaneously achieve computational efficiency and accurate confidence intervals. We illustrate the method for a copula-based Monte Carlo computation of claims written on a basket of underlying assets, and we test it numerically for Portfolio Default Options. For any number of underlying assets or names in a portfolio, the sensitivities of the option price with respect to all the pairwise correlations is obtained at a computational cost which is at most 4 times the cost of calculating the option value itself. For typical applications, this results in computational savings of several order of magnitudes with respect to standard methods.
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