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

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.

Type: Working paper
Date: le 07/06/2010
Research Cluster : Finance

See Also

Meet the Class: Global MBA January 2020
News
- 28-01-2020
This January wasn’t just the beginning of a new decade, but the start of another MBA...
BOOST YOUR CAREER
News
- 28-01-2020
A SCHOOL WITH AN INTERNATIONAL PERSPECTIVE With five campuses in three countries,...
FT RANKINGS 2020: EDHEC GLOBAL MBA RECOGNISED FOR VALUE, DIVERSITY AND INTERNATIONAL EXPERIENCE IN LATEST TOP 100 RANKINGS REPORT
News
- 27-01-2020
  Placed 28th worldwide for value for money by the FT and overall 88th, the intensive...
The EDHEC Business School Association and its Foundation announce the signature of an agreement for the sale of a 93% interest in Scientific Beta to Singapore Exchange Ltd.
News
- 24-01-2020
The transaction values Scientific Beta at €200m and is expected to be completed by the...