Options that allow the holder to extend the  maturity by paying an additional fixed amount found many applications in finance. Closed-form solution for these options first appeared in Longstaff (1990) for the case when  underlying asset follows a geometric Brownian motion with the constant interest rate and volatility. Unfortunately there are several typographical errors in the published formula for the holder-extendible put. These are subsequently repeated in textbooks, other papers and software. This short paperpresents a correct formula. Also, to generalize, the option price is derived for the case of  a geometric Brownian motion with the time-dependent drift and volatility  .
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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Options
Financial contracts with options
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contract
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solution for these options first appeared in Longstaff (1990)
solutions for the price of these options have appeared in the literature
A
the contract
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and volatility. Unfortunately there are several typographical errors in the published formula for the holder-extendible put. These are subsequently repeated in textbooks, other papers and software. This short paperpresents a correct formula. Also, to generalize,
, volatility, and non-negative "dividend" yield. In this paper,
A
the underlying asset that follows
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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