Streamlining Monte Carlo Simulation with the Quasi-Analytic Method : Analysis of a Path-Dependent Option Strategy

Trading strategies and contingent claims with path-dependent returns are difficult to model analytically. Monte Carlo simulation, the standard solution technique, is computationally expensive and provides a solution only for the specific parameter values used in the simulation. We present an alternative quot;quasi-analyticquot; procedure that combines the power and flexibility of the simulation approach with the computational efficiency of an analytical solution. Our method uses simulation results to construct an analytic function that provides an approximate mapping from the input parameters to the returns distribution function. This analytic function can then be used to estimate the returns distribution for other parameter values directly without further simulation. We illustrate the approach by analyzing the performance of a path-dependent long-term protective put strategy that requires rolling over a series of short-term options. The returns to the strategy depend on the investor's choice of put strike and rollover policy. We use our method to examine a risk-averse investor's optimal trading strategy, a problem that is time-consuming using standard Monte Carlo simulation. In one example, the simulation approach takes more than forty-five minutes to solve for just one particular volatility scenario, while our method provides the answer in a matter of seconds