OPTIMAL REPLICATION OF OPTIONS WITH TRANSACTIONS COSTS AND TRADING RESTRICTIONS

This paper analyzes the strategy that minimizes the initial cost of replicating a contingent claim in a market with transactions costs and trading constraints. The linear programming and two-stage backward recursive models developed are applicable to the replication of convex as well as nonconvex payoffs and to a portfolio of options with different maturities. The paper's formulation conveniently accounts for fixed and variable transactions costs, lot size constraints, and position limits on trading. The article shows that in the presence of trading frictions, it is no longer optimal to revise one's portfolio in each period. At the optimum, cash flows in excess of the desired ones may be generated. The optimal policy trades off the curvature of the payoff that is generated against the terminal slack.