Optimal Investment in Derivative Securities

Posted: 19 Mar 2001

See all articles by Peter Carr

Peter Carr

New York University Finance and Risk Engineering

Xing Jin

University of Maryland - Robert H. Smith School of Business

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business

Abstract

We consider the problem of optimal investment in a risky asset, and in derivatives written on the price process of this asset, when the underlying asset price process is a pure jump Levy process. The duality approach of Karatzas and Shreve is used to derive the optimal consumption and investment plans. In our economy, the optimal derivative payoff can be constructed from dynamic trading in the risky asset and in European options of all strikes. Specific closed forms illustrate the optimal derivative contracts when the utility function is in the HARA class and when the statistical and risk-neutral price processes are in the variance gamma (VG) class. In this case, we observe that the optimal derivative contract pays a function of the price relatives continuously through time.

Keywords: Levy process, market completeness, stochastic duality, option pricing, variance gamma model

JEL Classification: G11,C61

Suggested Citation

Carr, Peter P. and Jin, Xing and Madan, Dilip B., Optimal Investment in Derivative Securities. Finance and Stochastics, Vol. 5 Issue 1 . Available at SSRN: https://ssrn.com/abstract=257026

Peter P. Carr (Contact Author)

New York University Finance and Risk Engineering ( email )

6 MetroTech Center
Brooklyn, NY 11201
United States
9176217733 (Phone)

HOME PAGE: http://engineering.nyu.edu/people/peter-paul-carr

Xing Jin

University of Maryland - Robert H. Smith School of Business ( email )

Van Munching Hall
College Park, MD 20742-1815
United States

Dilip B. Madan

University of Maryland - Robert H. Smith School of Business ( email )

College Park, MD 20742-1815
United States
301-405-2127 (Phone)
301-314-9157 (Fax)

Register to save articles to
your library

Register

Paper statistics

Abstract Views
1,384
PlumX Metrics