最小平方蒙地卡羅法之平行化效能評估

Abstract

Option pricing is an important issue in financial computing. However, the early-exercise feature of American options makes their pricing more difficult than European options. To price American options using simulation, Longstaff and Schwartz presented a simple yet powerful simulation technique, named the least-squares Monte Carlo method. Least-squares Monte Carlo simulation involves huge amounts of path simulation, which makes it difficult to compute the price in a short amount of time. To solve this problem, this thesis divides the computation paths into threads and then compares the numerical results of the strategy, the original version and the trinomial tree. The outcome shows that the division strategy does not have much impact on the prices. After the numerical evaluation of the division strategy, the least-square Monte Carlo method is parallelized and evaluated on the speedup and efficiency. The results show that the parallelization of the least-squares Monte Carlo method provides considerable speedup without sacrificing numerical accuracy. The Longstaff-Schwartz algorithm is thus amenable to parallelism.