Optimal Timing to Purchase Options

SIAM Journal on Financial Mathematics, Vol. 2, No. 1, pp. 768-793, 2011

24 Pages Posted: 23 Aug 2010 Last revised: 12 Jan 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: September 20, 2010

Abstract

We study the optimal timing of derivative purchases in incomplete markets. In our model, an investor attempts to maximize the spread between her model price and the offered market price through optimally timing her purchase. Both the investor and the market value the options by risk-neutral expectations but under different equivalent martingale measures representing different market views. The structure of the resulting optimal stopping problem depends on the interaction between the respective market price of risk and the option payoff. In particular, a crucial role is played by the delayed purchase premium that is related to the stochastic bracket between the market price and the buyer's risk premia. Explicit characterization of the purchase timing is given for two representative classes of Markovian models: (i) defaultable equity models with local intensity; (ii) diffusion stochastic volatility models. Several numerical examples are presented to illustrate the results. Our model is also applicable to the optimal rolling of long-dated options and sequential buying and selling of options.

Keywords: optimal stopping, delayed purchase premium, martingale measures, risk premia

JEL Classification: G12, G13, D52, D81

Suggested Citation

Leung, Tim and Ludkovski, Mike, Optimal Timing to Purchase Options (September 20, 2010). SIAM Journal on Financial Mathematics, Vol. 2, No. 1, pp. 768-793, 2011. Available at SSRN: https://ssrn.com/abstract=1662804

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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