American options exercise boundary when the volatility changes randomly
type: Item
instance of: scholarly article
title: American options exercise boundary when the volatility changes randomly
zbMATH Open document ID: 0937.60039
published in: Applied Mathematics and Optimization
publication date: 2000-05-28T00:00:00Z
review text: The American put option exercise boundary is studied. It is shown that the put option premium in the Black and Scholes model [see \textit{F. Black} and \textit{M. Scholes}, J. Political Economy 81, 637-659 (1973)] is a one-to-one function of the volatility parameter. The paper focuses on the dependence of the optimal exercise boundary on the volatility parameter. A stochastic volatility model for the underlying asset, which generalizes the Black and Scholes model by allowing the volatility itself to be varying [see \textit{J. Hull} and \textit{A. White}, J. Finance 3, 281-300 (1987); \textit{L. Scott}, J. Financial and Quantitative Analysis 22, 419-438 (1987); \textit{J. Wiggins}, J. Financial Economics 19, 351-372 (1987)] is considered. It is proved that (i) the American put price function is continuously differentiable, (ii) there exists an optimal exercise boundary and (iii) the American put price function is strictly convex in the current underlying asset price in the continuation region. In the stochastic volatility model studied in the paper the exercise boundary is a function of the volatility variable. It is proved that the optimal exercise boundary is a decreasing function of the volatility.
Mathematics Subject Classification ID: 60G40
Mathematics Subject Classification ID: 91B28
Mathematics Subject Classification ID: 93E20
zbMATH DE Number: 1289884
zbMATH Keywords: incomplete markets
zbMATH Keywords: optimal stopping
zbMATH Keywords: viscosity solutions
author: Nizar Touzi
reviewed by: Krzysztof J. Szajowski
MaRDI profile type: Publication
full work available at URL: s002459900112
OpenAlex ID: W2032531578
Wikidata QID: Q127808108
DOI: 10.1007/S002459900112
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description: scientific article; zbMATH DE number 1289884