Hostname: page-component-7b7567c8c-fvjsw Total loading time: 0 Render date: 2026-11-14T22:00:36.603Z Has data issue: false hasContentIssue false
  • English
  • Français

A note on American options with varying exercise price

Published online by Cambridge University Press:  17 February 2009

J. N. Dewynne and
P. Wilmott
J. N. Dewynne
Affiliation:
Department of Mathematics, University of Southampton, Southampton, SO17 IBJ, England.
P. Wilmott
Affiliation:
Mathematical Inst., Oxford University, Oxford, England, and Dept. of Math., Imperial College, London, England.
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.

We examine the valuation of American options in a discrete time setting where the exercise price is known a priori but varies with time. (This is in contrast with the classical Black-Scholes [2] analysis, which lies in a continuous time framework and with constant exercise price.) In particular we consider a time series of exercise prices which are themselves a realisation of the share price random walk — that of the previous year, say.

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 37 , Issue 1 , July 1995, pp. 45 - 57
Copyright
Copyright © Australian Mathematical Society 1995

References

[1]Black, F., “The holes in Black-Scholes”, in “From Black-Scholes to black-holes”, (Risk/Finex, London, 1992).Google Scholar
[2]Black, F. and Scholes, M., “The pricing of options and corporate liabilities”, J. Pol. Economy 81 (1973) 637–659.CrossRefGoogle Scholar
[3]Cox, J. C. and Ross, S. A., “The pricing of options for jump processes”, Working paper no. 2–75, White, Rodney L. Center for Financial Research, University of Pennsylvania, (1975).Google Scholar
[4]Cox, J. C. and Ross, S. A., “The valuation of options for alternative stochastic processes”, J. Fin. Econ 3 (1976) 145–166.CrossRefGoogle Scholar
[5]Cox, J. C., Ross, S. A. and Rubinstein, M., “Option pricing: a simplified approach”, J. Fin. Econ (1979) 7 (1979) 229–263.CrossRefGoogle Scholar
[6]Cox, J. C. and Rubinstein, M., Options markets (Prentice-Hall, Englewood Cliffs, 1985).Google Scholar
[7]Crank, J. and Gupta, R. S., “A moving boundary problem arising from the diffusion of oxygen in absorbing tissue” J. Inst. Maths. Applic. 10 (1972) 19–33.CrossRefGoogle Scholar
[8]Crank, J., Free and moving boundary problems (Oxford University Press, Oxford, 1984).Google Scholar
[9]Dewynne, J. N., Howinson, S. D., Rupf, I. and Wilmott, P., “Some mathematical results in the pricing of American options”, Euro. J. Appl. Math. 4 (1993) 381–398.CrossRefGoogle Scholar
[10]Dewynne, J. N., Whalley, A. E. and Wilmott, P., “Path-dependent options and transaction costs”, Phil. Trans. R. Soc. Lond. A 347 (1994) 517–529.Google Scholar
[11]Elliott, C M. and Ockendon, J. R., Weak and variational methods for variational problems (Pitman, Boston, 1982).Google Scholar
[12]Harrison, J. M. and Pliska, S. R., “Martingales and stochastic integrals in the theory of continuous trading”, Stoch. Proc. Appl. 11 (1981) 261–271.CrossRefGoogle Scholar
[13]Hodges, S. D. and Neuberger, A., “Optimal replication of contingent claims under transaction costs”, Review of Futures Markets 8 (1989).Google Scholar
[14]Hull, J., Options, futures and other derivative securities (2nd ed.), (Prentice-Hall, Englewood Cliffs, 1993).Google Scholar
[15]Jacka, S. D., “Optimal stopping and the American put”, Math. Finan. 1 (1991) 1–14.CrossRefGoogle Scholar
[16]Jaillet, P., Lamberton, D. and Lapeyre, B., “Variational inequalities and die pricing of American options”, Acta Applicandae Mathematics (1990).CrossRefGoogle Scholar
[17]Leland, H. E., “Option pricing and replication with transaction costs”, Journal of Finance 15 (1985) 1283–1295.CrossRefGoogle Scholar
[18]Øksendal, B., Stochastic differential equations (Springer, 1992).CrossRefGoogle Scholar
[19]Peters, E. E., Chaos and order in the capital markets (Wiley, New York, 1991).Google Scholar
[20]Wilmott, P., Dewynne, J. N. and Howinson, S. D., Option pricing: mathematical models and computation (Oxford Financial Press, Oxford, 1993).Google Scholar