Hostname: page-component-78c5997874-g7gxr Total loading time: 0 Render date: 2024-11-10T12:14:36.656Z Has data issue: false hasContentIssue false
  • English
  • Français

Perpetual American put options in a level-dependent volatility model

Part of: Stochastic processes

Published online by Cambridge University Press:  14 July 2016

Erik Ekström
Erik Ekström*
Affiliation:
Uppsala University
*
∗Postal address: Department of Mathematics, Uppsala University, Box 480, 751 06 Uppsala, Sweden. Email address: ekstrom@math.uu.se
Get access Rights & Permissions [Opens in a new window]

Abstract

We find the explicit value of perpetual American put options in the constant elasticity of variance model using the concept of smooth fit. We show that the price is increasing in the volatility and convex in the underlying stock price. Moreover, as the model converges to the standard Black and Scholes model, the value of the put is shown to approach the ‘correct’ limit.

Keywords

Optimal stoppingoptionsvolatilityconstant elasticity of variance model

MSC classification

Primary: 60G40: Stopping times; optimal stopping problems; gambling theory
Type
Short Communications
Information
Journal of Applied Probability , Volume 40 , Issue 3 , September 2003 , pp. 783 - 789
Copyright
Copyright © Applied Probability Trust 2003 

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Cox, J. C., and Ross, S. R. (1976). The valuation of options for alternative stochastic processes. J. Financial Econom. 3, 145–166.CrossRefGoogle Scholar
Ekström, E. (2003). Properties of American option prices. Submitted.Google Scholar
El Karoui, N., Jeanblanc-Picqué, M., and Shreve, S. E. (1998). Robustness of the Black and Scholes formula. Math. Finance 8, 93–126.Google Scholar
Grigelionis, B. I., and Shiryaev, A. N. (1966). On the Stefan problem and optimal stopping rules for Markov processes. Theory Prob. Appl. 11, 541–558.Google Scholar
Hobson, D. G. (1998). Volatility misspecification, option pricing and superreplication via coupling. Ann. Appl. Prob. 8, 193–205.CrossRefGoogle Scholar
Karatzas, I. (1988). On the pricing of American options. Appl. Math. Optimization 17, 37–60.Google Scholar
Karatzas, I., and Shreve, S. E. (1998). Methods of Mathematical Finance. Springer, Berlin.Google Scholar
Karatzas, I., and Shreve, S. E. (2000). Brownian Motion and Stochastic Calculus, 2nd edn. Springer, Berlin.Google Scholar
McKean, H. P. (1965). A free-boundary problem for the heat equation arising from a problem in mathematical economics. Indust. Manag. Rev. 6, 32–39.Google Scholar