Streamlining Monte-Carlo Simulation with the Quasi-Analytic Method: An Analysis of a Path-Dependent Option Strategy
Posted: 23 Jul 1998
Date Written: September 1995
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 alternate "quasi-analytic" procedure that combines the power of the simulation approach with the computational efficiency of an analytical solution. Our method uses simulation results to construct an analytic function that maps the input parameters to the returns distribution function. This analytic function can then be used to directly estimate the returns distribution for other parameter values 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 exceedingly time-consuming using standard Monte Carlo simulation. For example, the simulation approach takes more than 45 minutes to solve for just one particular volatility scenario. Our method provides the answer in a matter of seconds.
JEL Classification: G13, C15
Suggested Citation: Suggested Citation