A MONTE CARLO FILTERING APPROACH FOR ESTIMATING THE TERM STRUCTURE OF INTEREST RATES

AKIHIKO TAKAHASHI^{1} AND SEISHO SATO^{2}

1Graduate School of Mathematical Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro-ku, Tokyo 153-8914, Japan

2The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan

(Received April 17, 2000; revised August 10, 2000)

Abstract. We develop new methodology for estimation of general class of term structure models based on a Monte Carlo filtering approach. We utilize the generalized state space model which can be naturally applied to the estimation of the term structure models based on the Markov state processes. It is also possible to introduce measurement errors in the general way without any bias. Moreover, the Monte Carlo filter can be applied even to the models in which the zero-coupon bonds’ prices can not be analytically obtained. As an example, we apply the method to LIBORs (London Inter Bank Offered Rates) and interest rates swaps in the Japanese market and show the usefulness of our approach.

Key words and phrases: Generalized state sapce model, Monte Carlo integration, interest rate model, self-organizing method.