Pricing and Hedging of Contingent Claims in the Presence of Extraneous Risk

Given an underlying complete financial market, we study the pricing and hedging of contingent claims whose payoffs may depend on the occurrence of extraneous, non market events. After a detailed analysis of the arbitrage pricing and almost sure hedging of such claims, we specialize our framework to the study of examples involving bilateral counterparty credit risk. Relying on these examples, we advocate the need for alternative pricing rules and study one that embeds the pricing problem into the agent's global portfolio/consumption decision: the utility-based pricing rule. Existence and consistency of derived pricing rule associated with general utility functions are established. The non linear dependence of the prices on contingent claims, initial capital and the size of the position are also studied and relations with the companion concept of fair price introduced by M. Davis are investigated.