A Note on Delta Hedging in Markets with Jumps

16 Pages Posted: 26 Mar 2011

See all articles by Aleksandar Mijatovic

Aleksandar Mijatovic

Imperial College London

Mikhail Urusov

University of Ulm - Department of Mathematics and Economics

Date Written: March 25, 2011

Abstract

Modeling stock prices via jump processes is common in financial markets. In practice, to hedge a contingent claim one typically uses the so-called delta-hedging strategy. This strategy stems from the Black-Merton-Scholes model where it perfectly replicates contingent claims. From the theoretical viewpoint, there is no reason for this to hold in models with jumps. However in practice the delta-hedging strategy is widely used and its potential shortcoming in models with jumps is disregarded since such models are typically incomplete and hence most contingent claims are non-attainable. In this note we investigate a complete model with jumps where the delta-hedging strategy is well-defined for regular payoff functions and is uniquely determined via the risk-neutral measure. In this setting we give examples of (admissible) delta-hedging strategies with bounded discounted value processes, which nevertheless fail to replicate the respective bounded contingent claims. This demonstrates that the deficiency of the delta-hedging strategy in the presence of jumps is not due to the incompleteness of the model but is inherent in the discontinuity of the trajectories.

Keywords: Delta hedging, Black-Merton-Scholes model, models with jumps

JEL Classification: G12, G13

Suggested Citation

Mijatovic, Aleksandar and Urusov, Mikhail, A Note on Delta Hedging in Markets with Jumps (March 25, 2011). Available at SSRN: https://ssrn.com/abstract=1795268 or http://dx.doi.org/10.2139/ssrn.1795268

Aleksandar Mijatovic (Contact Author)

Imperial College London ( email )

Department of Mathematics
180 Queen's Gate
London, SW7 2AZ
United Kingdom

HOME PAGE: http://www3.imperial.ac.uk/people/a.mijatovic

Mikhail Urusov

University of Ulm - Department of Mathematics and Economics ( email )

Helmholzstrasse
Ulm, D-89081
Germany

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