多因子模型下担保债务凭证拉普拉斯定价方法

Collateralized Debt Obligations' Pricing Based on Laplace Transform in Multifactor Models

担保债务凭证(CDOs)的基础资产池复杂相关性通常需要多因子Copula模型拟合,但Monte Carlo模拟对于多因子模型的计算效率不高,难以准确估计大额损失事件的发生概率及预期损失.Laplace逆变换数值方法适用于风险管理中的多因子Copula模型,通过逆变换数值方法计算资产条件损失的Laplace变换卷积,得到资产池损失分布,对任意阈值y,该方法同时适用于估计违约概率P(L>y)及期望值E[L∧y],数值实验表明该方法对小概率事件的估计效率有很大提升.

The multifactor version of Copula models is useful in fitting the complex correlation structure among the base portfolio of collateralized debt obligations（CDOs）. However, plain Monte Carlo simulation is quite incapable of accurately measuring rare but significant loss events. This paper provides a fast numerical inversion of conditional Laplace transform in multifactor models. The method is capable of estimating loss probability P （L 〉 y ） and expected loss E[L ∧ y]. Numerical examples illustrate the efficiency of the method, especially when handling rare events.