A Transaction Cost Convergence Result for General Hedging Strategies

This paper generalizes the result of Leland (1985) to hedging strategies that use not only the underlying but all kinds of otions. These hedging strategies are a generalization of static hedging. In addition, the result is valid for all shapes of payoff, including path-dependent. Two cases of hedging methods are studied. The first one, as in Leland, assumes rehedging takes place at fixed time intervals. The second one supposes rehedging takes place when the delta moves by more than a fixed proportion. The pricing of securities in that frame can be done by solving a non-linear partial differential equation, and optimal hedging strategies, using various kinds of options, can be found so as to minimize transaction costs