The Least-Squares Method for American Option Pricing

This article presents how to use the least-squares (LS) regression method to price the American options on basis of the algorithm in a paper by Clement, Lamberton & Protter[1]. The key to LS is the approximation of the conditional expectation functions which determine the optimal exercise strategy. In this paper, through the detailed description of the algorithm and presentation of convergence, it shows how to estimate the conditional expectation by using the LS to value the American options. Moreover, we also compare the simulation results with the historical data and experiment with alternative polynomials to analyze testing results. Acknowledgements First of all, we give the greatest thanks to our supervisor, Professor. Maciej Klimek. Thank you for offering us this challenging and interesting topic to help us complete our master thesis in financial mathematics program and for your patience and suggestions in the revision of this paper. Secondly, we would like to give sincere thanks to all teachers in Department of Mathematics. Particularly, we need to thank Erik Ekström and Prof. Johan Tysk since we learn so much relevant knowledge from financial mathematics II and III, which provides the prerequisite for our thesis. Last but not least, we owe the honest thanks to our parents. They support us not only in the studying, but also in our lives. Their endless love and care help us overcome the difficulties and always make us feel confident. Thank you!! We love you forever!