When pricing Bermudan derivatives by regression-based methods, foresight bias will appear in lower bounds when using a single simulation to estimate the exercise strategy and to compute lower bounds. In this paper, we propose a new method to remove this kind of bias without introducing an independent simulation. Numerical results indicate that the goodness of our method is comparable to that of using independent simulations. In addition, this method can be parallelized and enhanced by local regression. These improvements boost the accuracy and the time efficiency of lower bounds.
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