In the Black–Scholes model, consider the problem of selecting a change of drift which minimizes the variance of Monte Carlo estimators for prices of path-dependent options.
Employing large deviations techniques, the asymptotically optimal change of drift is identified as the solution to a one-dimensional variational problem, which may be reduced to the associated Euler–Lagrange differential equation.
Closed-form solutions for geometric and arithmetic average Asian options are provided.
Monte Carlo methods Variance reduction Importance sampling Large deviations
Dupuis, P., Ellis, R.S.: A Weak Convergence Approach to the Theory of Large Deviations. Wiley Series in Probability and Statistics: Probability and Statistics. Wiley, New York (1997)
Dupuis, P., Wang, H.: Importance sampling, large deviations, and differential games. Stoch. Stoch. Rep. 76, 481–508 (2004)