Holder-extendible European option: corrections and extensions
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.
Keywords
Cite
@article{arxiv.1010.0090,
title = {Holder-extendible European option: corrections and extensions},
author = {Pavel V. Shevchenko},
journal= {arXiv preprint arXiv:1010.0090},
year = {2015}
}