Holder-extendible European option

corrections and extensions

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Abstract

Financial contracts with options that allow the holder to extend the contract maturity by paying an additional fixed amount have 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 for the underlying asset follows a geometric Brownian motion with constant interest rate, volatility and nonnegative dividend yield. In this paper, option price is derived for the case of the underlying asset that follows a geometric Brownian motion with time-dependent drift and volatility, which is more important for real life applications. The option price formulae are derived for the case of a drift that includes nonnegative or negative dividend. The latter yields a solution type that is new to the literature. A negative dividend corresponds to a negative foreign interest rate for foreign exchange options, or storage costs for commodity options. It may also appear in pricing options with transaction costs or real options, where the drift is larger than the interest rate.
Original languageEnglish
Pages (from-to)359-372
Number of pages14
JournalANZIAM Journal
Volume56
Issue number4
DOIs
Publication statusPublished - Apr 2015
Externally publishedYes

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Keywords

  • Exotic options
  • Extendible maturities
  • Geometric Brownian motion.
  • Holder-extendible option

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