Download this Paper Open PDF in Browser

A Note on the Suboptimality of Path-Dependent Pay-Offs in Levy Markets

17 Pages Posted: 30 Oct 2007 Last revised: 14 Feb 2012

Steven Vanduffel

Vrije Universiteit Brussel (VUB)

Andrew Chernih

affiliation not provided to SSRN

Mateusz Maj

affiliation not provided to SSRN

Wim Schoutens

KU Leuven - Department of Mathematics

Date Written: November 6, 2008

Abstract

Cox & Leland (2000) used techniques from the field of stochastic control theory to show that in the particular case of a Brownian motion for the asset log-returns risk averse decision makers with a fixed investment horizon prefer path-independent pay-offs over path-dependent ones.

In this note we provide a novel and simple proof for the Cox & Leland result and we will extend it to general Levy markets in case pricing is based on the Esscher transform (exponential tilting). It is also shown that in these markets optimal path-independent pay-offs are increasing with the underlying final asset value. We provide examples that allow explicit verification of our theoretical findings and also show that the inefficiency cost of path-dependent pay-offs can be significant.

Our results indicate that path-dependent investment pay-offs, the use of which is widespread in financial markets, do not offer good value from the investor's point of view.

Keywords: Financial Structured Product, CPPI, Asian Option, Optimal investment, Mean Variance, Markowitz, Lévy Process, Exponential tilting, CAPM, Esscher transform

Suggested Citation

Vanduffel, Steven and Chernih, Andrew and Maj, Mateusz and Schoutens, Wim, A Note on the Suboptimality of Path-Dependent Pay-Offs in Levy Markets (November 6, 2008). Final version in Applied Mathematical Finance, Vol. 16, No. 4, pp 315-330 . Available at SSRN: https://ssrn.com/abstract=1025803

Steven Vanduffel (Contact Author)

Vrije Universiteit Brussel (VUB) ( email )

Pleinlaan 2
Brussels, Brabant 1050
Belgium

HOME PAGE: http://www.stevenvanduffel.com

Andrew Chernih

affiliation not provided to SSRN ( email )

No Address Available

Mateusz Maj

affiliation not provided to SSRN ( email )

Wim Schoutens

KU Leuven - Department of Mathematics ( email )

Celestijnenlaan 200 B
Leuven, B-3001
Belgium

Paper statistics

Downloads
222
Rank
116,063
Abstract Views
702