Hostname: page-component-8448b6f56d-xtgtn Total loading time: 0 Render date: 2024-04-23T12:57:56.441Z Has data issue: false hasContentIssue false
  • English
  • Français

APPROXIMATE SOLUTIONS FOR THE BRITISH PUT OPTION AND ITS OPTIMAL EXERCISE BOUNDARY

Part of: Mathematical finance

Published online by Cambridge University Press:  22 January 2016

JOANNA GOARD
JOANNA GOARD*
Affiliation:
School of Mathematics and Applied Statistics, University of Wollongong, Wollongong, NSW 2522, Australia email joanna@uow.edu.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.

British put options are financial derivatives with an early exercise feature whereby on payoff, the holder receives the best prediction of the European put payoff under the hypothesis that the true drift of the stock price is equal to a contract drift. In this paper, we derive simple analytic approximations for the optimal exercise boundary and the option valuation, valid for short expiry times – which is a common feature of most options traded in the market. Empirical results show that the approximations provide accurate results for expiries of at least up to two months.

Keywords

British optionsfree boundary problemsanalytic approximations

MSC classification

Primary: 91G20: Derivative securities
Type
Research Article
Information
The ANZIAM Journal , Volume 57 , Issue 3 , January 2016 , pp. 222 - 243
Copyright
© 2016 Australian Mathematical Society 

References

Alobaidi, G. and Mallier, R., “Asymptotic analysis of shout options close to expiry”, ISRN Appl. Math. 2014 (2014) 920385, 8 pages; doi:10.1155/2014/920385.Google Scholar
Black, F. and Scholes, M., “The pricing of options and corporate liabilities”, J. Polit. Econ. 81 (1973) 637–659; http://www.jstor.org/stable/1831029.Google Scholar
Detemple, J., American-style derivatives: valuation and computation, CRC Financial Mathematical Series (Chapman and Hall, New York, 2005).CrossRefGoogle Scholar
Goard, J., “Exact solutions for a strike reset put option and a shout call option”, Math. Comput. Modelling 55 (2012) 1787–1797; doi:10.1016/j.mcm.2011.11.033.CrossRefGoogle Scholar
Kwok, Y. K., Mathematical models of financial derivatives (Springer, Singapore, 1998).Google Scholar
Maplesoft, Maple 12 Users Manual (Maplesoft, Waterloo, Canada, 2008).Google Scholar
Peskir, G. and Samee, F., “The British put option”, Appl. Math. Finance 18 (2011) 537–563; doi:10.1080/1350486X.2011.591167.Google Scholar
Tao, L. N., “The analyticity of solutions of the Stefan problem”, Arch. Ration. Mech. Anal. 72 (1980) 285–301; doi:10.1007/BF00281593.CrossRefGoogle Scholar
Zhang, J. E. and Li, T., “Pricing and hedging American options analytically: a perturbation method”, Math. Finance 20 (2010) 59–87; doi:10.1111/j.1467-9965.2009.00389.x.CrossRefGoogle Scholar
Zhu, S.-P., “An exact and explicit solution for the valuation of American put options”, Quant. Finance 6 (2006) 229–242; doi:10.1080/14697680600699811.Google Scholar
Zhu, S.-P., “On various quantitative approaches for pricing American options”, New Math. Nat. Comput. 7 (2011) 313–332; doi:10.1142/S1793005711001950.Google Scholar