The Optimal Method for Pricing Bermudan Options by Simulation

Abstract

Least-squares methods allow to price Bermudan-style options by Monte Carlo simulation. They are based on estimating the option continuation value by least-squares. We show that the Bermudan option price is maximized when this continuation value is estimated near the exercise boundary, which is equivalent to implicitly estimate the optimal exercise boundary by using the value-matching condition. Localizing is the key difference with regression methods but fundamental to take optimal exercise decisions, and requires to estimate the continuation value by iterating local least-squares (since we estimate and localize the exercise boundary at the same time). In the numerical exercise, in agreement with this optimality, the new prices or lower-bounds (i) easily improve upon the prices reported by other methods and (ii) are very close to the associated dual upper-bounds. We also study the method's convergence.