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Holder-extendible European option: corrections and extensions

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  • Pavel V. Shevchenko

Abstract

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount found many applications in finance. Closed-form solutions for the price of these options have appeared in the literature for the case when the contract underlying asset follows a geometric Brownian motion with the constant interest rate, volatility, and non-negative "dividend" yield. In this paper, the option price is derived for the case of the underlying asset that follows a geometric Brownian motion with the time-dependent drift and volatility which is important to use the solutions in real life applications. The formulas are derived for the drift that may include non-negative or negative "dividend" yield. The latter case results in a new solution type that has not been studied in the literature. Several typographical errors in the formula for the holder-extendible put, typically repeated in textbooks and software, are corrected.

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  • Pavel V. Shevchenko, 2010. "Holder-extendible European option: corrections and extensions," Papers 1010.0090, arXiv.org, revised Sep 2014.
    • Handle: RePEc:arx:papers:1010.0090
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    References listed on IDEAS

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    1. Longstaff, Francis A, 1990. "Pricing Options with Extendible Maturities: Analysis and Applications," Journal of Finance, American Finance Association, vol. 45(3), pages 935-957, July.
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