Pricing American Swaption by Least Square Approach with Modified Discounting Factor

We use the Least- Square Monte-Carlo simulation approach (Longstaff, F., E. Schwartz, 2001) to evaluate the American interest rate swaptions. Before this approach was developed, Monte-Carlo simulation could only be used in pricing the European options. Unable to help make optimal decisions for early exercise, it couldn’t apply to American options pricing. LSM could solve the problems above, provide a pathwise approximation to the optimal stopping rule that maximize the value of the American option regardless of if the underlying asset is path-dependent or not and how many stochastic variables are involved in the moving process.
In previous studies about American swaptions, people are used to estimate cash flows’ present value by fixed, predetermined discounting factor without concerning how the discounter will change during the contract period. In this thesis, we take this situation into account to help improve the precision of the estimated value, and then analyze the influence occurred by our discounting rate adjustment.