Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-05T10:22:55.711Z Has data issue: false hasContentIssue false
  • English
  • Français

HOLDER-EXTENDIBLE EUROPEAN OPTION: CORRECTIONS AND EXTENSIONS

Part of: Mathematical finance

Published online by Cambridge University Press:  02 July 2015

PAVEL V. SHEVCHENKO
PAVEL V. SHEVCHENKO*
Affiliation:
CSIRO, Locked Bag 17, North Ryde, NSW, 1670, Australia email Pavel.Shevchenko@csiro.au
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

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.

Keywords

exotic optionsextendible maturitiesholder-extendible optiongeometric Brownian motion

MSC classification

Primary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 56 , Issue 4 , April 2015 , pp. 359 - 372
Copyright
© 2015 Australian Mathematical Society 

References

Chateau, J. P. and Wu, J., “Basel-2 capital adequacy: computing the ‘fair’ capital charge for loan commitment ‘true’ credit risk”, Int. Rev. Financ. Anal. 16 (2007) 1–21; doi:10.1016/j.irfa.2004.12.002.CrossRefGoogle Scholar
Chung, Y. P. and Johnson, H., “Extendible options: the general case”, Finance Res. Lett. 8 (2011) 15–20; doi:10.1016/j.frl.2010.09.003.CrossRefGoogle Scholar
Harrison, J. M. and Pliska, S., “Martingales and stochastic integrals in the theory of continuous trading”, Stochastic Process. Appl. 11 (1981) 215–260; doi:10.1016/0304-4149(81)90026-0.CrossRefGoogle Scholar
Haug, E. G., The complete guide to options pricing formulas (McGraw-Hill, New York, 1998).Google Scholar
Ibrahim, S. N. I., O’Hara, J. G. and Constantinou, N., “Pricing extendible options using the fast fourier transform”, Math. Probl. Eng. 2014 (2014) 1–7; doi:10.1155/2014/831470.Google Scholar
Longstaff, F. A., “Pricing options with extendible maturities: analysis and applications”, J. Finance 45 (1990) 935–957; doi:10.2307/2328800.CrossRefGoogle Scholar