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Importance Sampling for Credit Portfolio Risk with Risk Factors Having t-Copula

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  • Rongda Chen

    (China Academy of Financial Research, Zhejiang University of Finance and Economics, Hangzhou 310018, China2School of Finance, Zhejiang University of Finance and Economics, Hangzhou 310018, China3Coordinated Innovation Center of Wealth Management and Quantitative Investment of Zhejiang University of Finance and Economics, Hangzhou 310018, China4Center for Research of Regulation and Policy of Zhejiang Province, Hangzhou 310018, China)

  • Ze Wang

    (School of Finance, Zhejiang University of Finance and Economics, Hangzhou 310018, China)

  • Lean Yu

    (School of Economics and Management, Beijing University of Chemical Technology, Beijing 100029, China)

Abstract

This paper proposes an efficient simulation method for calculating credit portfolio risk when risk factors have a heavy-tailed distributions. In modeling heavy tails, its features of return on underlying asset are captured by multivariate t-Copula. Moreover, we develop a three-step importance sampling (IS) procedure in the t-copula credit portfolio risk measure model for further variance reduction. Simultaneously, we apply the Levenberg–Marquardt algorithm associated with nonlinear optimization technique to solve the problem that estimates the mean-shift vector of the systematic risk factors after the probability measure change. Numerical results show that those methods developed in the t-copula model can produce large variance reduction relative to the plain Monte Carlo method, to estimate more accurately tail probability of credit portfolio loss distribution.

Suggested Citation

  • Rongda Chen & Ze Wang & Lean Yu, 2017. "Importance Sampling for Credit Portfolio Risk with Risk Factors Having t-Copula," International Journal of Information Technology & Decision Making (IJITDM), World Scientific Publishing Co. Pte. Ltd., vol. 16(04), pages 1101-1124, July.
    • Handle: RePEc:wsi:ijitdm:v:16:y:2017:i:04:n:s0219622017500201
    DOI: 10.1142/S0219622017500201
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    References listed on IDEAS

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    1. Jones, E Philip & Mason, Scott P & Rosenfeld, Eric, 1984. "Contingent Claims Analysis of Corporate Capital Structures: An Empirical Investigation," Journal of Finance, American Finance Association, vol. 39(3), pages 611-625, July.
    2. Grundke, Peter, 2009. "Importance sampling for integrated market and credit portfolio models," European Journal of Operational Research, Elsevier, vol. 194(1), pages 206-226, April.
    3. Rosenberg, Joshua V. & Schuermann, Til, 2006. "A general approach to integrated risk management with skewed, fat-tailed risks," Journal of Financial Economics, Elsevier, vol. 79(3), pages 569-614, March.
    4. Kjersti Aas & Ingrid Hobaek Haff, 2006. "The Generalized Hyperbolic Skew Student's t-Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 4(2), pages 275-309.
    5. Huang, Yan & Kou, Gang & Peng, Yi, 2017. "Nonlinear manifold learning for early warnings in financial markets," European Journal of Operational Research, Elsevier, vol. 258(2), pages 692-702.
    6. Paul Glasserman & Wanmo Kang & Perwez Shahabuddin, 2008. "Fast Simulation of Multifactor Portfolio Credit Risk," Operations Research, INFORMS, vol. 56(5), pages 1200-1217, October.
    7. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2002. "Portfolio Value‐at‐Risk with Heavy‐Tailed Risk Factors," Mathematical Finance, Wiley Blackwell, vol. 12(3), pages 239-269, July.
    8. Kole, Erik & Koedijk, Kees & Verbeek, Marno, 2007. "Selecting copulas for risk management," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2405-2423, August.
    9. Chan, Joshua C.C. & Kroese, Dirk P., 2010. "Efficient estimation of large portfolio loss probabilities in t-copula models," European Journal of Operational Research, Elsevier, vol. 205(2), pages 361-367, September.
    10. Paul Glasserman & Jingyi Li, 2005. "Importance Sampling for Portfolio Credit Risk," Management Science, INFORMS, vol. 51(11), pages 1643-1656, November.
    11. Achal Bassamboo & Sandeep Juneja & Assaf Zeevi, 2008. "Portfolio Credit Risk with Extremal Dependence: Asymptotic Analysis and Efficient Simulation," Operations Research, INFORMS, vol. 56(3), pages 593-606, June.
    12. Paul Glasserman & Philip Heidelberger & Perwez Shahabuddin, 2000. "Variance Reduction Techniques for Estimating Value-at-Risk," Management Science, INFORMS, vol. 46(10), pages 1349-1364, October.
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    Cited by:

    1. Matthias Fischer & Thorsten Moser & Marius Pfeuffer, 2018. "A Discussion on Recent Risk Measures with Application to Credit Risk: Calculating Risk Contributions and Identifying Risk Concentrations," Risks, MDPI, vol. 6(4), pages 1-28, December.
    2. Zhong, Li-Xin & Xu, Wen-Juan & Chen, Rong-Da & Zhong, Chen-Yang & Qiu, Tian & Ren, Fei & He, Yun-Xing, 2018. "Self-reinforcing feedback loop in financial markets with coupling of market impact and momentum traders," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 493(C), pages 301-310.
    3. Huang, Zhenzhen & Kwok, Yue Kuen & Xu, Ziqing, 2024. "Efficient algorithms for calculating risk measures and risk contributions in copula credit risk models," Insurance: Mathematics and Economics, Elsevier, vol. 115(C), pages 132-150.

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