Abstracts

Many problems in financial engineering involve the estimation of unknown conditional expectations across time. In the econometrics literature a well-known solution is estimation through sieve. This approach has been exploited in Least Squares Monte Carlo (LSMC) where a simulation-based regression approach is taken. Unlike conventional algorithms where the value function is regressed on a set of basis functions valued at an earlier time, the “Regress-Later” method regresses the value function on a set of basis functions valued at the same time. The conditional expectation across time is then computed exactly for each basis function. We provide sufficient conditions under which we derive the convergence rate of Regress-Later estimators. Importantly, our results hold on non-compact sets. We show that the Regress-Later method is capable of converging significantly faster than conventional algorithms and provide an explicit example. Achieving faster convergence speed provides a strong motivation for using Regress-Later methods in estimating conditional expectations across time.