Holder-extendible European option: corrections and extensions

Authors

  • Pavel Shevchenko CSIRO Mathematics, Informatics and Statistics

DOI:

https://doi.org/10.21914/anziamj.v56i0.8804

Keywords:

exotic options, extendible maturities, holder-extendible option, geometric Brownian motion

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. doi:10.1017/S1446181115000097

Published

2015-07-14

Issue

Section

Articles for Printed Issues