Pricing of path-dependent American options by Monte Carlo simulation

In this paper, we evaluate floating-rate bond options, a variant of path-dependent American options, by Monte Carlo simulation. Assuming that the underlying state variable is Markovian, we show that the price of a floating-rate bond option satisfies a dynamic programming equation. The continuation value in the dynamic programming problem is represented by a conditional expectation. It is shown that the conditional expectation can be transformed to an unconditional expectation, using the Malliavin calculus, which in turn enables us to evaluate the price of the floating-rate bond option by Monte Carlo methods. Some numerical examples are given to demonstrate the usefulness of our method.