Forward Indifference Valuation of American Options

Stochastics: An International Journal of Probability and Stochastic Processes, 84(5-6): 741-770, 2012

30 Pages Posted: 10 Apr 2010 Last revised: 27 Jan 2015

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering

Thaleia Zariphopoulou

University of Texas at Austin (Mathematics and IROM)

Date Written: June 1, 2011

Abstract

We analyze the American option valuation problem with the forward performance criterion introduced by Musiela and Zariphopoulou (2008). In this framework, utility evolves forward in time without reference to a specific future time horizon. Moreover, risk preferences change with stochastic market conditions, which is natural as investors are clearly more risk averse in economic downtimes. We examine two applications: the valuation of American options with stochastic volatility and the modeling of early exercises of American-style employee stock options. Finally, we introduce the marginal forward performance price introduced by Davis (1997). Among others, we find that, for arbitrary preferences, the marginal forward indifference price is always independent of the investor's wealth and is represented as the claim's risk-neutral price under the minimal martingale measure.

Keywords: Indifference pricing, forward investment performance, American options, employee stock options, utility maximization

JEL Classification: C60, G11, G13, J33

Suggested Citation

Leung, Tim and Sircar, Ronnie and Zariphopoulou, Thaleia, Forward Indifference Valuation of American Options (June 1, 2011). Stochastics: An International Journal of Probability and Stochastic Processes, 84(5-6): 741-770, 2012 , Available at SSRN: https://ssrn.com/abstract=1587057 or http://dx.doi.org/10.2139/ssrn.1587057

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States

HOME PAGE: http://faculty.washington.edu/timleung/

Ronnie Sircar

Princeton University - Department of Operations Research and Financial Engineering ( email )

Princeton, NJ 08544
United States

Thaleia Zariphopoulou

University of Texas at Austin (Mathematics and IROM) ( email )

CBA 5.202
Austin, TX 78712
United States

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