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Interactions of Logistic Distribution to Credit Valuation Adjustment: A Study on the Associated Expected Exposure and the Conditional Value at Risk

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Listed:
  • Yanlai Song

    (College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China)

  • Stanford Shateyi

    (Department of Mathematics and Applied Mathematics, School of Mathematical and Natural Sciences, University of Venda, P. Bag X5050, Thohoyandou 0950, South Africa)

  • Jianying He

    (College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China)

  • Xueqing Cui

    (College of Science, Zhongyuan University of Technology, Zhengzhou 450007, China)

Abstract

In Basel III, the credit valuation adjustment (CVA) was given, and it was discussed that a bank covers mark-to-market losses for expected counterparty risk with a CVA capital charge. The purpose of this study is threefold. Using the logistic distribution, it is shown how the expected exposure can be derived for an interest rate swap. Secondly, the risk measure of VaR is contributed for the CVA under this distribution. Thirdly, generalizations for the CVA VaR and CVA CVaR are given by considering both the credit spread and the expected positive exposure to follow the logistic distributions with different parameters. Finally, several simulations are provided to uphold the theoretical discussions.

Suggested Citation

  • Yanlai Song & Stanford Shateyi & Jianying He & Xueqing Cui, 2022. "Interactions of Logistic Distribution to Credit Valuation Adjustment: A Study on the Associated Expected Exposure and the Conditional Value at Risk," Mathematics, MDPI, vol. 10(20), pages 1-15, October.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:20:p:3828-:d:944323
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