Complete Markets

Abstract

A market model is said to be complete if any financial derivative admits a replicating strategy. The completeness of a market model ensures that any derivative security can be priced by arbitrage and hedged through dynamic trading in primary traded assets. In a complete market model, not only call and put options but also any exotic option can be replicated by dynamic trading in the primary securities. The Cox, Ross, and Rubinstein binomial model of the stock price is complete. The classic Black and Scholes options pricing model enjoys the property of completeness under suitable technical assumptions