BFS 2002

Poster Presentation

Mean-Variance Hedging with Proportional Transaction Costs

Ales Cerny

The paper gives a closed-form dynamic programming solution to the discrete time mean-variance hedging problem with proportional transaction costs that can be easily implemented on a Markov chain. It then compares the performance of the dynamically optimal strategy with the Leland and Black-Scholes hedging strategies for realistic (leptokurtic) return distribution and transaction costs. We find that the dynamically optimal strategy outperforms Leland strategy for high transaction costs (1%), but that the replication error of the best hedging strategy is very high. Furthermore, in terms of performance there is little difference between hedging once a day and once a week. On the theoretical level this paper generalizes and combines the analyses of Leland (1985) and Schweizer (1995).