Response surface methodology for simulating hedging and trading strategies

Suppose that one wishes to evaluate the distribution of profit and loss (P&L) resulting from a dynamic trading strategy. A straightforward method is to simulate thousands of paths (i.e., time series) of relevant financial variables and to track the resulting P&L at every time at which the trading strategy rebalances its portfolio. In many cases, this requires numerical computation of portfolio weights at every rebalancing time on every path, for example, by a nested simulation performed conditional on market conditions at that time on that path. Such a two-level simulation could involve many millions of simulations to compute portfolio weights, and thus be too computationally expensive to attain high accuracy. We show that response surface methodology enables a more efficient simulation procedure: in particular, it is possible to do far fewer simulations by using kriging to model portfolio weights as a function of underlying financial variables.