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Weak Convergence of Path-Dependent SDEs in Basket CDS Pricing with Contagion Risk

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  • Yao Tung Huang
  • Qingshuo Song
  • Harry Zheng

Abstract

We investigate the computational aspects of the basket CDS pricing with counterparty risk under a credit contagion model of multinames. This model enables us to capture the systematic volatility increases in the market triggered by a particular bankruptcy. The drawback of this problem is its analytical complication due to its path-dependent functional, which bears a potential failure in its convergence of numerical approximation under standing assumptions. In this paper we find sufficient conditions for the desired convergence of the functionals associated with a class of path-dependent stochastic differential equations. The main ingredient is to identify the weak convergence of the approximated solution to the underlying path-dependent stochastic differential equation.

Suggested Citation

  • Yao Tung Huang & Qingshuo Song & Harry Zheng, 2015. "Weak Convergence of Path-Dependent SDEs in Basket CDS Pricing with Contagion Risk," Papers 1506.00082, arXiv.org, revised May 2016.
    • Handle: RePEc:arx:papers:1506.00082
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    References listed on IDEAS

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    1. Harry Zheng, 2013. "Contagion models a la carte: which one to choose?," Quantitative Finance, Taylor & Francis Journals, vol. 13(3), pages 399-405, February.
    2. Metzler, Adam, 2010. "On the first passage problem for correlated Brownian motion," Statistics & Probability Letters, Elsevier, vol. 80(5-6), pages 277-284, March.
    3. Tim Leung & Qingshuo Song & Jie Yang, 2013. "Outperformance portfolio optimization via the equivalence of pure and randomized hypothesis testing," Finance and Stochastics, Springer, vol. 17(4), pages 839-870, October.
    4. Chan, K. S. & Stramer, O., 1998. "Weak consistency of the Euler method for numerically solving stochastic differential equations with discontinuous coefficients," Stochastic Processes and their Applications, Elsevier, vol. 76(1), pages 33-44, August.
    5. Jia-Wen Gu & Wai-Ki Ching & Tak-Kuen Siu & Harry Zheng, 2013. "On pricing basket credit default swaps," Quantitative Finance, Taylor & Francis Journals, vol. 13(12), pages 1845-1854, December.
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