Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties

Journal of Financial Engineering, vol. 2, issue 1, 2015

25 Pages Posted: 30 Nov 2013 Last revised: 29 Mar 2015

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Yoshihiro Shirai

University of Maryland College Park

Date Written: July 4, 2014

Abstract

This paper studies the risk-adjusted optimal timing to liquidate an option at the prevailing market price. In addition to maximizing the expected discounted return from option sale, we incorporate a path-dependent risk penalty based on shortfall or quadratic variation of the option price up to the liquidation time. We establish the conditions under which it is optimal to immediately liquidate or hold the option position through expiration. Furthermore, we study the variational inequality associated with the optimal stopping problem, and prove the existence and uniqueness of a strong solution. A series of analytical and numerical results are provided to illustrate the non-trivial optimal liquidation strategies under geometric Brownian motion (GBM) and exponential Ornstein-Uhlenbeck models. We examine the combined effects of price dynamics and risk penalty on the sell and delay regions for various options. In addition, we obtain an explicit closed-form solution for the liquidation of a stock with quadratic penalty under the GBM model.

Keywords: optimal liquidation, options, shortfall risk, quadratic risk penalty

Suggested Citation

Leung, Tim and Shirai, Yoshihiro, Optimal Derivative Liquidation Timing Under Path-Dependent Risk Penalties (July 4, 2014). Journal of Financial Engineering, vol. 2, issue 1, 2015, Available at SSRN: https://ssrn.com/abstract=2361506 or http://dx.doi.org/10.2139/ssrn.2361506

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/

Yoshihiro Shirai

University of Maryland College Park ( email )

4176 Campus Drive
College Park, MD 20740
United States

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