基于伴随算法微分的快速相关Greeks
Fast Correlation Greeks by Adjoint Algorithmic Differentiation
摘要：
我们展示了如何伴随算法微分（AAD）允许一个非常有效的计算相关性风险的期权价格计算与蒙特卡罗模拟。在建设中的一个关键点是使用binning同时实现计算效率和准确的置信区间。我们说明了基于Copula的蒙特卡罗计算的方法，写在一篮子标的资产的索赔，我们测试它的数字为投资组合违约期权。对于投资组合中的任何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灵敏度以最多4倍于计算期权价值本身的计算成本获得。对于典型的应用，这导致相对于标准方法的几个数量级的计算节省。
英文摘要：
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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