CONTINGENT CLAIMS AND MARKET COMPLETENESS IN A STOCHASTIC VOLATILITY MODEL

In an incomplete market framework, contingent claims are of particular interest since they improve the market efficiency. This paper address es the problem of market completeness when trading in contingent claim s is allowed. We extend recent results by Bajeux and Rochet (1996) in a stochastic volatility model to the case where the asset price and it s volatility variations are correlated. We also relate the ability of a given contingent claim to complete the market to the convexity of it s price function in the current asset price. This allows us to state o ur results for general contingent claims by examining the convexity of their ''admissible arbitrage prices.''.