Mean-variance hedging strategies in discrete time and continuous state space

Abstract

In this paper we consider the mean-variance hedging problem of a continuous state space financial model with the rebalancing strategies for the hedging portfolio taken at discrete times. An expression is derived for the optimal self-financing mean-variance hedging strategy problem, considering any given payoff in an incomplete market environment. To some extent, the paper extends the work of Cerný [1] to the case in which prices may assume any value within a continuous state space, a situation that more closely reflects real market conditions. An expression for the “fair hedging price” for a derivative with any given payoff is derived. Closed-form solutions for both the “fair hedging price” and the optimal control for the case of a European call option are obtained. Numerical results indicate that the proposed method is consistently better than the Black and Scholes approach, often adopted by practitioners.