Efficient Variance Reduction with Least-Squares Monte Carlo Pricing

This paper examines the efficiency of standard variance reduction techniques across option characteristics when pricing American-style call and put options with the Least-Squares Monte Carlo algorithm of Longstaff & Schwartz (2001). Our numerical experiments evaluate the efficiency of antithetic sampling, control variates, importance sampling, and combinations thereof. Whereas most of the American option pricing literature has focused on either put or call options individually, we employ the symmetry relation of McDonald & Schroder (1998) to compare performance for pairs of call and put options whose solution coincide. Our results first show that variance reduction is generally more efficient for put than call options and that control variates is the most efficient stand-alone method. We also find that marginal gains in efficiency are typically achieved by combining variance reduction techniques, though some techniques may interact conflictingly. Finally, since valuation of American-style call options can be improved by pricing symmetric put options instead (Stentoft 2019), we demonstrate that drastic reductions in the standard deviation of the call is obtained by combining all three variance reduction techniques in a symmetric pricing approach, which reduces the standard deviation by a factor of over 20 for long maturity call options on highly volatile assets.