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A Mellin Transform Approach to the Pricing of Options with Default Risk

Author

Listed:
  • Sun-Yong Choi

    (Gachon University)

  • Sotheara Veng

    (Royal University of Phnom Penh)

  • Jeong-Hoon Kim

    (Yonsei University)

  • Ji-Hun Yoon

    (Pusan National University)

Abstract

The stochastic elasticity of variance model introduced by Kim et al. (Appl Stoch Models Bus Ind 30(6):753–765, 2014) is a useful model for forecasting extraordinary volatility behavior which would take place in a financial crisis and high volatility of a market could be linked to default risk of option contracts. So, it is natural to study the pricing of options with default risk under the stochastic elasticity of variance. Based on a framework with two separate scales that could minimize the number of necessary parameters for calibration but reflect the essential characteristics of the underlying asset and the firm value of the option writer, we obtain a closed form approximation formula for the option price via double Mellin transform with singular perturbation. Our formula is explicitly expressed as the Black–Scholes formula plus correction terms. The correction terms are given by the simple derivatives of the Black–Scholes solution so that the model calibration can be done very fast and effectively.

Suggested Citation

  • Sun-Yong Choi & Sotheara Veng & Jeong-Hoon Kim & Ji-Hun Yoon, 2022. "A Mellin Transform Approach to the Pricing of Options with Default Risk," Computational Economics, Springer;Society for Computational Economics, vol. 59(3), pages 1113-1134, March.
    • Handle: RePEc:kap:compec:v:59:y:2022:i:3:d:10.1007_s10614-021-10121-w
    DOI: 10.1007/s10614-021-10121-w
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    References listed on IDEAS

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    1. Fouque,Jean-Pierre & Papanicolaou,George & Sircar,Ronnie & Sølna,Knut, 2011. "Multiscale Stochastic Volatility for Equity, Interest Rate, and Credit Derivatives," Cambridge Books, Cambridge University Press, number 9780521843584.
    2. Sun‐Yong Choi & Jeong‐Hoon Kim & Ji‐Hun Yoon, 2016. "The Heston model with stochastic elasticity of variance," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 32(6), pages 804-824, November.
    3. Johnson, Herb & Stulz, Rene, 1987. "The Pricing of Options with Default Risk," Journal of Finance, American Finance Association, vol. 42(2), pages 267-280, June.
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    7. Mao‐Wei Hung & Yu‐Hong Liu, 2005. "Pricing vulnerable options in incomplete markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 25(2), pages 135-170, February.
    8. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
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    Cited by:

    1. Ha, Mijin & Kim, Donghyun & Yoon, Ji-Hun, 2024. "Valuing of timer path-dependent options," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 215(C), pages 208-227.

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