Sequential Static-Dynamic Hedging for Long-Term Derivatives

Procedia Computer Science, Volume 9, 2012, pp.1211-1218

8 Pages Posted: 28 Mar 2013 Last revised: 16 Apr 2014

See all articles by Tim Leung

Tim Leung

University of Washington - Department of Applied Math

Date Written: March 26, 2013

Abstract

This paper presents a new methodology for hedging long-term financial derivatives written on an illiquid asset. The proposed hedging strategy combines dynamic trading of a correlated liquid asset (e.g. the market index) and static positions in market-traded options such as European puts and calls. Moreover, since most market-traded options are relatively short-term, it is necessary to conduct the static hedge sequentially over time till the long-term derivative expires. This sequential static-dynamic hedging strategy leads to the study of a stochastic control problem and the associated Hamilton-Jacobi-Bellman PDEs and variational inequalities. A series of transformations allow us to simplify the problem and compute the optimal hedging strategy.

Keywords: portfolio optimization, employee stock options,optimal stopping, Hamilton-Jacobi-Bellman PDE, variational inequality

JEL Classification: G12, G13, C68

Suggested Citation

Leung, Tim, Sequential Static-Dynamic Hedging for Long-Term Derivatives (March 26, 2013). Procedia Computer Science, Volume 9, 2012, pp.1211-1218, Available at SSRN: https://ssrn.com/abstract=2240072

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/

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