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Pricing Basket Spread Options With Default Risk Under GARCH‐Jump Models

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  • Dingding Dong
  • Xianda Qian
  • Xingchun Wang

Abstract

In this article, we consider basket spread options with default risk in a pricing model, where GARCH‐jump processes are employed to describe the dynamics of all the underlying assets, and default risk is incorporated in a reduced form model. After successfully deriving the approximate pricing formula, we utilize the average cumulative default rates provided by Moody's spanning from 1970 to 2015 to estimate the parameters in the default intensity. Finally, we illustrate the impact of jump risk and default risk on basket spread options after checking the accuracy and efficiency of the approximate prices via Monte Carlo simulation methods.

Suggested Citation

  • Dingding Dong & Xianda Qian & Xingchun Wang, 2025. "Pricing Basket Spread Options With Default Risk Under GARCH‐Jump Models," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 45(5), pages 441-454, May.
    • Handle: RePEc:wly:jfutmk:v:45:y:2025:i:5:p:441-454
    DOI: 10.1002/fut.22574
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    References listed on IDEAS

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Ornthanalai, Chayawat, 2014. "Lévy jump risk: Evidence from options and returns," Journal of Financial Economics, Elsevier, vol. 112(1), pages 69-90.
    3. Christoffersen, Peter & Jacobs, Kris & Ornthanalai, Chayawat, 2012. "Dynamic jump intensities and risk premiums: Evidence from S&P500 returns and options," Journal of Financial Economics, Elsevier, vol. 106(3), pages 447-472.
    4. Wang, Xingchun & Zhang, Han, 2022. "Pricing basket spread options with default risk under Heston–Nandi GARCH models," The North American Journal of Economics and Finance, Elsevier, vol. 59(C).
    5. Zakoian, Jean-Michel, 1994. "Threshold heteroskedastic models," Journal of Economic Dynamics and Control, Elsevier, vol. 18(5), pages 931-955, September.
    6. Madan, Dilip B & Seneta, Eugene, 1990. "The Variance Gamma (V.G.) Model for Share Market Returns," The Journal of Business, University of Chicago Press, vol. 63(4), pages 511-524, October.
    7. Zelei Li & Dan Tang & Xingchun Wang, 2023. "Valuing basket-spread options with default risk under Hawkes jump-diffusion processes," The European Journal of Finance, Taylor & Francis Journals, vol. 29(12), pages 1406-1431, August.
    8. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
    9. Yung-Ming Shiu & Pai-Lung Chou & Jen-Wen Sheu, 2013. "A closed-form approximation for valuing European basket warrants under credit risk and interest rate risk," Quantitative Finance, Taylor & Francis Journals, vol. 13(8), pages 1211-1223, July.
    10. Jean-François Bégin & Christian Dorion & Geneviève Gauthier, 2020. "Idiosyncratic Jump Risk Matters: Evidence from Equity Returns and Options," The Review of Financial Studies, Society for Financial Studies, vol. 33(1), pages 155-211.
    11. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
    12. Li, Zelei & Wang, Xingchun, 2020. "Valuing spread options with counterparty risk and jump risk," The North American Journal of Economics and Finance, Elsevier, vol. 54(C).
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