Discrete-time implementation of continuous-time portfolio strategies

Optimal portfolio strategies are easy to compute in continuous-time models. In reality trading is discrete, so that these optimal strategies cannot be implemented properly. When the investor follows a naive discretization strategy, i.e. when he implements the optimal continuous-time strategy in discrete time, he will suffer a utility loss. For a variety of models, we analyze this discretization error in a simulation study. We find that time discreteness can be neglected when only the stock and the money market account are traded, even in models with stochastic volatility and jumps. On the other hand, when derivatives are traded the utility loss due to discrete trading can be much larger than the utility gain from having access to derivatives. To benefit from derivatives, the investor has to rebalance his portfolio at least daily.