Accounting for Risk Aversion in Derivatives Purchase Timing

Mathematics & Financial Economics, 2012

24 Pages Posted: 5 Sep 2011 Last revised: 5 Mar 2012

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Michael Ludkovski

University of California, Santa Barbara

Date Written: January 4, 2012

Abstract

We study the problem of optimal timing to buy/sell derivatives by a risk-averse agent in incomplete markets. Adopting the exponential utility indifference valuation, we investigate this timing flexibility and the associated delayed purchase premium. This leads to a stochastic control and optimal stopping problem that combines the observed market price dynamics and the agent's risk preferences. Our results extend recent work on indifference valuation of American options, as well as the authors' first paper (Leung and Ludkovski, SIAM J. Fin. Math., 2011). In the case of Markovian models of contracts on non-traded assets, we provide analytical characterizations and numerical studies of the optimal purchase strategies, with applications to both equity and credit derivatives.

Keywords: sequential purchase timing, indifference pricing, exponential utility, stochastic control with optimal stopping

JEL Classification: G12, G13, C68

Suggested Citation

Leung, Tim and Ludkovski, Mike, Accounting for Risk Aversion in Derivatives Purchase Timing (January 4, 2012). Mathematics & Financial Economics, 2012. Available at SSRN: https://ssrn.com/abstract=1922191 or http://dx.doi.org/10.2139/ssrn.1922191

Tim Leung (Contact Author)

University of Washington - Department of Applied Math ( email )

Lewis Hall 217
Department of Applied Math
Seattle, WA 98195
United States
9253381749 (Phone)

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

Mike Ludkovski

University of California, Santa Barbara ( email )

Santa Barbara, CA 93106
United States

HOME PAGE: http://www.pstat.ucsb.edu/faculty/ludkovski

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