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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. It first provides 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, it presents an analytical expression for the optimal hedging strategy and the corresponding option price. It also provides a quantitative measure of the residual risk over the life of the option.

Author(s) :

Lionel Martellini, Vincent Milhau

Summary :

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. It first provides 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, it presents an analytical expression for the optimal hedging strategy and the corresponding option price. It also provides a quantitative measure of the residual risk over the life of the option.

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Type : Working paper
Date : 14/06/2010
Keywords :

Asset Pricing