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Vulnerable American options


  • Peter Klein
  • Jun Yang


Purpose - The purpose of this paper is to extend the models of Johnson and Stulz, Klein and Klein and lnglis to analyse the properties of vulnerable American options. Design/methodology/approach - The presented model allows default prior to the maturity of the option based on a barrier which is linked to the payoff on the option. Various measures of risk denoted by the standard Greek letters are studied, as well as additional measures that arise because of the vulnerability. Findings - The paper finds that the delta of a vulnerable American put does not always increase with the price of the underlying asset, and may be significantly smaller than that of a non-vulnerable put. Because of deadweight costs associated with bankruptcy, delta and gamma are undefined for some values of the underlying asset. Rho may be considerably higher while vega may be smaller than for non-vulnerable options. Also, the probability of early exercise for vulnerable American options is higher and the price of the underlying asset at which this is optimal depends on the degree of credit risk of the option writer. Originality/value - This paper makes a contribution to understanding the effect of credit risk on option valuation.

Suggested Citation

  • Peter Klein & Jun Yang, 2010. "Vulnerable American options," Managerial Finance, Emerald Group Publishing, vol. 36(5), pages 414-430, April.
  • Handle: RePEc:eme:mfipps:v:36:y:2010:i:5:p:414-430

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    References listed on IDEAS

    1. Black, Fischer & Cox, John C, 1976. "Valuing Corporate Securities: Some Effects of Bond Indenture Provisions," Journal of Finance, American Finance Association, vol. 31(2), pages 351-367, May.
    2. Hull, John & White, Alan, 1990. "Valuing Derivative Securities Using the Explicit Finite Difference Method," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 25(01), pages 87-100, March.
    3. Merton, Robert C, 1974. "On the Pricing of Corporate Debt: The Risk Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 29(2), pages 449-470, May.
    4. 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.
    5. Klein, Peter, 1996. "Pricing Black-Scholes options with correlated credit risk," Journal of Banking & Finance, Elsevier, vol. 20(7), pages 1211-1229, August.
    6. Hull, John & White, Alan, 1995. "The impact of default risk on the prices of options and other derivative securities," Journal of Banking & Finance, Elsevier, vol. 19(2), pages 299-322, May.
    7. Klein, Peter & Inglis, Michael, 2001. "Pricing vulnerable European options when the option's payoff can increase the risk of financial distress," Journal of Banking & Finance, Elsevier, vol. 25(5), pages 993-1012, May.
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    Cited by:

    1. Xu, Weidong & Xu, Weijun & Li, Hongyi & Xiao, Weilin, 2012. "A jump-diffusion approach to modelling vulnerable option pricing," Finance Research Letters, Elsevier, vol. 9(1), pages 48-56.


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