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Explicit expressions to counterparty credit exposures for Forward and European Option

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  • Li, Shuang
  • Peng, Cheng
  • Bao, Ying
  • Zhao, Yanlong

Abstract

With the fast development of over the counter (OTC) derivatives market, counterparty credit risk (CCR) has become one of the main risks that can even affect the survival of banks. As a result, it is essential to measure and manage CCR exposures. Giant financial institutions apply numerical methods such as the Monte Carlo to calculate exposures. However, the numerical methods usually cost a significant amount of time, and some advanced algorithms like distributed and parallel processing are usually used to accelerate the calculation. Nevertheless, for small banks, they cannot afford the calculation cost. In order to make small banks manage CCR more efficiently, this paper puts forward analytic models to measure CCR exposures and derives the explicit expressions to exposures for Forward contract and European Option, which are represented in the OTC market. The explicit expressions to credit exposures for Forward contract are derived under the assumption that the underlying market risk factors follow Geometric Brown Motion. For European Option case, the problem turns to be difficult since the analytic formula involves double-definite integral of Gaussian function that cannot be simplified into elementary functions. An approximating normal distribution function with integrability is proposed, then the analytic approximations of European Call Option’s credit exposures and maximum errors are presented.

Suggested Citation

  • Li, Shuang & Peng, Cheng & Bao, Ying & Zhao, Yanlong, 2020. "Explicit expressions to counterparty credit exposures for Forward and European Option," The North American Journal of Economics and Finance, Elsevier, vol. 52(C).
    • Handle: RePEc:eee:ecofin:v:52:y:2020:i:c:s1062940819302475
    DOI: 10.1016/j.najef.2019.101130
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    References listed on IDEAS

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    1. Hunzinger, Chadd B. & Labuschagne, Coenraad C.A., 2014. "The Cox, Ross and Rubinstein tree model which includes counterparty credit risk and funding costs," The North American Journal of Economics and Finance, Elsevier, vol. 29(C), pages 200-217.
    2. Hui, Cho-Hoi & Lo, Chi-Fai & Chau, Po-Hon, 2018. "Exchange rate dynamics and US dollar-denominated sovereign bond prices in emerging markets," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 109-128.
    3. Patrik Karlsson & Shashi Jain & Cornelis W. Oosterlee, 2016. "Counterparty Credit Exposures for Interest Rate Derivatives using the Stochastic Grid Bundling Method," Applied Mathematical Finance, Taylor & Francis Journals, vol. 23(3), pages 175-196, May.
    4. Michael S. Gibson, 2005. "Measuring counterparty credit exposure to a margined counterparty," Finance and Economics Discussion Series 2005-50, Board of Governors of the Federal Reserve System (U.S.).
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    Citations

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    Cited by:

    1. Shi, Ruoshi & Zhao, Yanlong & Bao, Ying & Peng, Cheng, 2022. "Sensitivity-based Conditional Value at Risk (SCVaR): An efficient measurement of credit exposure for options," The North American Journal of Economics and Finance, Elsevier, vol. 62(C).
    2. Gijs Mast & Xiaoyu Shen & Fang Fang, 2023. "Fast calculation of Counterparty Credit exposures and associated sensitivities using fourier series expansion," Papers 2311.12575, arXiv.org.

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