Short-term interest rate models: Valuing interest rate derivatives using a Monte-Carlo approach

This paper provides an accessible description and several examples of how to use Monte-Carlo simulation to value interest rate derivatives when the short rate follows an arbitrary time series process. We compare the values of various interest rate derivatives using closed-form solutions (when available), the Hull and White (1994) trinomial tree procedure, and a Monte-Carlo simulation technique. We show that the simulation technique can be applied to more complex short rate processes by examining short rate models where the dynamics are too complicated for any tree or lattice approach and closed-form valuation formulae are unavailable. In a practical empirical setting, we weigh the advantages and disadvantages of the simulation approach against competing approaches.