Pricing American Options on Bonds using Least Squares Simulation∗

In this project we discuss Least Square MonteCarlo methods for valuing American options on bonds. We investigate when we use different base functions, vary the number of base functions and sample paths, how the option price vary. From experiments, we know that we have better choose simple base functions, like Shifted Legendre polynomial; for the balance between time and accuracy issue, we suggest to use 3 or 4 terms of base functions and generate sample paths between 10,000 to 100,000. And we also use three different numerical methods for simulating stochastic models. As the explicit Euler method is dominant in the extant literature of computational finance, it is strongly recommended to use numerical methods with higher convergence order to reduce the discretization error. In this project we use the Milstein method for simulating the one-factor by default.