Option Pricing and Hedging in the Presence of Cross-Hedge Risk

This paper addresses the question of option pricing and hedging when the underlying asset is not available for dynamic trading, and some other asset is used as a substitute.

Author(s) :

Lionel Martellini

Professor of Finance, EDHEC Business SchoolScientific Director, EDHEC-Risk Institute

Vincent Milhau

Research Engineer, EDHEC-Risk Institute

Presentation :

We first provide an overview of the various hedging methodologies that can be used in this incomplete market setting, distinguishing between self-financing and non-self-financing strategies. Focussing on a local risk-minimization criterion, we present an analytical expression for the optimal hedging strategy and the corresponding option price. We also provide a quantitative measure of the residual risk over the life of the option. We find that the use of the optimal strategy induces a much smaller replication error compared to the replication error induced by a naive Black-Scholes strategy, especially for low levels of the correlation between the underlying asset and the substitute. In the absence of transaction costs, we also find that cross hedge risk is more substantial than the risk induced by discrete trading for reasonable parameter values. While this result implies that trading in the substitute can only be rationalised for exceedingly high correlations, the presence of (higher levels of) transaction costs is likely, however, to make trading in the actual underlying asset a prohibitively costly alternative.
Pdf
Option Pricing and Hedging in the Presence of Cross-Hedge Risk...
(3.85 MB)
Type : Working paper
Date : le 07/06/2010
Extra information : Pour plus d'informations, nous vous prions de vous adresser à Joanne Finlay, Direction de la recherche de l'EDHEC [ joanne.finlay@edhec.edu ] Les opinions exprimées sont celles des auteurs et n'engagent pas la responsabilité de l'EDHEC.
Research Cluster : Finance

See Also

OTHERWISE#4 is online !
- 23-03-2017
One of EDHEC’s hallmarks is “being where it is not expected to be” and OTHERWISE...
Support the new generation of students
- 20-03-2017
Support the new generation of students Act for EDHEC! Many Alumni in the UK have...
Emmanuel Metais named new Dean of EDHEC Business School
- 17-03-2017
EDHEC Business School is pleased to announce Emmanuel Métais’s appointment as the new...
MSc in Data Analytics & Digital Business: a new master designed to bridge the gap between data specialists and decision makers
- 13-03-2017
EDHEC Business School is pleased to announce the launch of a new MSc in Data Analytics...