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An analytical GARCH valuation model for spread options with default risk

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  • Song, Shiyu
  • Tang, Dan
  • Xu, Guangli
  • Yin, Xunbai

Abstract

In this paper, an analytical pricing formula for spread options with credit default risk is derived. Assets are set within discrete-time CAPM markets and Heston–Nandi GARCH processes are adopted for capturing the variance dynamics of asset returns. The proposed model decomposes the risk of all assets into idiosyncratic and systematic parts, and considers the impacts on the default intensity of market fluctuations. A corresponding theoretical framework of discrete-time credit risk modeling in reduced-form is also provided. We incorporate the credit risk and systematic factor into an affine-GARCH valuation model and utilize Fourier transform techniques to obtain the analytic spread option prices. Finally, the empirical results and numerical analysis for different model parameters are displayed.

Suggested Citation

  • Song, Shiyu & Tang, Dan & Xu, Guangli & Yin, Xunbai, 2023. "An analytical GARCH valuation model for spread options with default risk," International Review of Economics & Finance, Elsevier, vol. 83(C), pages 1-20.
    • Handle: RePEc:eee:reveco:v:83:y:2023:i:c:p:1-20
    DOI: 10.1016/j.iref.2022.08.013
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    References listed on IDEAS

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    More about this item

    Keywords

    GARCH; Spread options; Default risk;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing

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