Under the traditional hedging framework, there exist two assumptions that are signicantly impractical for the real world: the continuous trading assumption and the zero transaction cost assumption. In reality we are constrained to readjust our hedging portfolio only at certain xed discrete time points and we may need to pay certain costs associated with the transaction for rebalancing procedures. In this article we will break these two assumptions and adopt a dynamic discrete hedging strategy with trading costs taken into consideration. Under this framework the hedging result will consequently be not perfect any longer. A low rebalancing frequency will lead to a large hedging error while a higher rebalancing frequency will reduce the hedging error at the cost of higher transaction costs. Given the constraints of discrete trading and transaction costs, we have to make a decision on the choice of optimal hedging frequency. Meanwhile, we are also interested in measuring the hedging performance under these constraints.

To implement the simulation of dynamic hedging with transaction costs, we have to estimate the sensitivity at all the rebalancing nodes on every sample path. When our hedging target has a discontinuous payo function, estimating sensitivity becomes very dicult since many existing methods cannot cope with its discontinuity here. Several sensitivity approximating algorithms for options with discontinuous payo functions have been proposed in recent years. They are computationally attractive where nested simulations are not necessary. However we are not satised with all current sensitivity estimating methods because they are still too computationally demanding for our dynamic hedging framework.

In this thesis we propose regression based sensitivity estimating methods with high computational eciency while still being able to deliver reliable results. It can be applied to products with various payo functions and show great advantage when eciency is the main issue of problem. Our methods can also handle higher order derivatives like option gamma, which is useful for hedging practice and risk management.

Based on our sensitivity estimating methods, we use simulation experiments to examine the hedging performance and try to make an optimal decision on hedging frequency.