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Semi-Analytical Pricing for General Default Intensity Models

Author

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  • Ryan Parker
  • Mark Stedman
  • Luca Capriotti

Abstract

Using the path-integral formalism, we develop an accurate and easy-to-compute semi-analytical approximation for a general class of {default intensity} models. We illustrate the accuracy of the method by presenting results for the Black-Karasinski model for which the proposed approximation provides remarkably accurate results, even in regimes of high volatility and multi-year time horizons. The accuracy and the computational efficiency of the proposed approximation makes it a viable alternative to fully numerical schemes for a variety of applications in econometrics and derivatives pricing, including the computation of XVA for credit products. As a practical example, we consider the pricing of a quanto Credit Default Swap (CDS) under stochastic intensity of default and an FX devaluation model.

Suggested Citation

  • Ryan Parker & Mark Stedman & Luca Capriotti, 2026. "Semi-Analytical Pricing for General Default Intensity Models," Papers 2606.21800, arXiv.org.
    • Handle: RePEc:arx:papers:2606.21800
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    References listed on IDEAS

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    1. Beáta Stehlíková & Luca Capriotti, 2014. "An Effective Approximation For Zero-Coupon Bonds And Arrow–Debreu Prices In The Black–Karasinski Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(06), pages 1-16.
    2. Andrzej Daniluk & Rafał Muchorski, 2016. "Approximations Of Bond And Swaption Prices In A Black–Karasiński Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-32, May.
    3. Fabricio Tourrucoo & Patrick S. Hagan & Gilberto F. Schleiniger, 2007. "Approximate Formulas for Zero-coupon Bonds," Applied Mathematical Finance, Taylor & Francis Journals, vol. 14(3), pages 207-226.
    4. Mark Stedman & Luca Capriotti, 2024. "A Path Integral Approach for Time-Dependent Hamiltonians with Applications to Derivatives Pricing," Papers 2408.02064, arXiv.org.
    5. Damiano Brigo & Nicola Pede & Andrea Petrelli, 2019. "Multi-Currency Credit Default Swaps," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 22(04), pages 1-35, June.
    6. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
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