Pricing and Hedging in the Presence of Extraneous Risks

by Pierre Collin-Dufresne of University of California Berkeley, and
Julien Hugonnier of HEC Université de Lausanne

June 2007

Abstract: Given an underlying complete financial market, we study contingent claims whose payoffs may depend on the occurrence of nonmarket events. We first investigate the almost-sure hedging of such claims. In particular, we obtain new representations of the hedging prices and provide necessary and sufficient conditions for a claim to be marketed. The analysis of various examples then leads us to investigate alternative pricing rules. We choose to embed the pricing problem into the agent's portfolio decision and study reservation prices. We establish the existence and consistency of this pricing rule in a semimartingale model. We characterize the nonlinear dependence of the reservation price with respect to both the agent's initial capital and the size of her position. The fair price arises as a limiting case.

AMS Classification: 60H30,91B38,93E20.

Keywords: Nonmarket risks, Incomplete markets, Utility based pricing, Event risk, Fair price.

Published in: Stochastic Processes and their Applications, Vol. 117, No. 6, (June 2007), pp. 742-765.

Previously titled: On the Pricing and Hedging of Contingent Claims in the Presence of Extraneous Risks

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