Dynamic Hedging in Incomplete Markets: A Simple Solution

Abstract

We provide fully analytical, optimal dynamic hedges in incomplete markets by employing the traditional minimum-variance criterion. Our hedges are in terms of generalized “Greeks” and naturally extend no-arbitrage–based risk management in complete markets to incomplete markets. Whereas the literature characterizes either minimum-variance static, myopic, or dynamic hedges from which a hedger may deviate unless able to precommit, our hedges are time-consistent. We apply our results to derivatives replication with infrequent trading and determine hedges and replication values, which reduce to generalized Black-Scholes expressions in specific settings. We also investigate dynamic hedging with jumps, stochastic correlation, and portfolio management with benchmarking.