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An ETD Method for Vulnerable American Options

Author

Listed:
  • Rafael Company

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain)

  • Vera N. Egorova

    (Departamento de Matemática Aplicada y Ciencias de la Computación, Universidad de Cantabria, Avenida de los Castros, s/n, 39005 Santander, Spain)

  • Lucas Jódar

    (Instituto de Matemática Multidisciplinar, Universitat Politècnica de València, Camino de Vera, s/n, 46022 Valencia, Spain)

Abstract

This paper introduces the exponential time differencing (ETD) technique as a numerical method to efficiently solve vulnerable American options pricing. We address several challenges, including removing cross-derivative terms through appropriate transformations, treating early-exercise opportunities using the penalty method, and substituting fixed boundary conditions with corresponding one-sided finite differences. The proposed method is shown to be both accurate and efficient through numerical experiments, which also compare the results with existing methods and analyze the numerical stability and convergence rate.

Suggested Citation

  • Rafael Company & Vera N. Egorova & Lucas Jódar, 2024. "An ETD Method for Vulnerable American Options," Mathematics, MDPI, vol. 12(4), pages 1-14, February.
    • Handle: RePEc:gam:jmathe:v:12:y:2024:i:4:p:602-:d:1340635
    as

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    References listed on IDEAS

    as
    1. Lung-Fu Chang & Mao-Wei Hung, 2006. "Valuation of vulnerable American options with correlated credit risk," Review of Derivatives Research, Springer, vol. 9(2), pages 137-165, September.
    2. repec:eme:mfppss:v:36:y:2010:i:5:p:414-430 is not listed on IDEAS
    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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    6. Geske, Robert & Johnson, Herb E, 1984. "The American Put Option Valued Analytically," Journal of Finance, American Finance Association, vol. 39(5), pages 1511-1524, December.
    7. R. Company & V. N. Egorova & L. Jódar, 2014. "Solving American Option Pricing Models by the Front Fixing Method: Numerical Analysis and Computing," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, April.
    8. 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.
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