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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
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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 

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