基于条件蒙特卡罗方法的信用违约互换合约定价

多标的资产违约相关性结构的度量及其联合违约时间的模拟是信用违约互换合约定价的关键.Copula函数和蒙特卡罗模拟是解决此关键问题的有力工具,被广泛应用于信用衍生品定价.本文基于因子t-copula模型,结合条件蒙特卡罗模拟,构建了计算第7n次信用违约互换合约的条件蒙特卡罗算法.该算法能够捕捉多标的资产违约的尾部相关性,更准确地度量标的资产组合的违约风险及提高违约事件的模拟效率.数值结果表明,在考虑尾部相关性的情形下,采用重要抽样技术的JK算法和改进的JK算法是不稳定的,不能达到减方差的目的;而本文新构建的定价算法更稳定,在高斯copula和t-copula模型下,都能够有效减小估计量的方差,提高信用违约互换合约的定价精度和可靠性.

Pricing credit default swap based on conditional Monte Carlo method

The main challenge of pricing credit default swaps is to properly capture the dependence structure of all underlying assets and then simulate their joint default times. Copula functions and Monte Carlo simulation are widely adopted to address these two problems respectively and price credit derivatives. Based on a newly developed factor student t-copula model and conditional Monte Carlo simulation, this study proposed a conditional Monte Carlo algorithm for valuating CDS which not only can capture the tail dependence among the underlying assets and measure their joint default risk more precisely, but also can improve the simulation efficiency of default events. Our results demonstrated that, compared with the famous JK and improved JK methods, the proposed algorithm is much more stable even in the t-copula model and can significantly improve the pricing accuracy as well.