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Applications of Gram-Charlier expansion and bond moments for pricing of interest rates and credit risk

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  • Keiichi Tanaka
  • Takeshi Yamada
  • Toshiaki Watanabe

Abstract

The purpose of this paper is to demonstrate the powerful and flexible applicability of the Gram-Charlier expansion to pricing of a wide variety of interest rate related products involving interest rate risk and credit risk. In this paper, we develop easily implemented approximations of the prices of several derivatives; swaptions, CMS, CMS options, and vulnerable options. Associated with the default risk, a survival contingent forward measure is constructed.

Suggested Citation

  • Keiichi Tanaka & Takeshi Yamada & Toshiaki Watanabe, 2010. "Applications of Gram-Charlier expansion and bond moments for pricing of interest rates and credit risk," Quantitative Finance, Taylor & Francis Journals, vol. 10(6), pages 645-662.
    • Handle: RePEc:taf:quantf:v:10:y:2010:i:6:p:645-662
    DOI: 10.1080/14697680903193371
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    References listed on IDEAS

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    Cited by:

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    3. Marco Di Francesco & Kevin Kamm, 2022. "On the deterministic-shift extended CIR model in a negative interest rate framework," Papers 2203.07458, arXiv.org.
    4. Lin, Shin-Hung & Huang, Hung-Hsi & Li, Sheng-Han, 2015. "Option pricing under truncated Gram–Charlier expansion," The North American Journal of Economics and Finance, Elsevier, vol. 32(C), pages 77-97.
    5. Marco Di Francesco & Kevin Kamm, 2022. "On the Deterministic-Shift Extended CIR Model in a Negative Interest Rate Framework," IJFS, MDPI, vol. 10(2), pages 1-26, May.
    6. De Clerk, Luke & Savel’ev, Sergey, 2022. "AI algorithms for fitting GARCH parameters to empirical financial data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 603(C).
    7. Sofiane Aboura & Didier Maillard, 2016. "Option Pricing Under Skewness and Kurtosis Using a Cornish–Fisher Expansion," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 36(12), pages 1194-1209, December.
    8. Chenyu Zhao & Misha van Beek & Peter Spreij & Makhtar Ba, 2021. "Polynomial Approximation of Discounted Moments," Papers 2111.00274, arXiv.org.
    9. Schlögl, Erik, 2013. "Option pricing where the underlying assets follow a Gram/Charlier density of arbitrary order," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 611-632.
    10. Kazuki Nagashima & Tsz-Kin Chung & Keiichi Tanaka, 2014. "Asymptotic Expansion Formula of Option Price Under Multifactor Heston Model," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 21(4), pages 351-396, November.

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