A yield-factor model of interest rates-英文文献.pdf

Mathemciricd Finatiw, Vol. 6. No. 4 (October l996), 379406 A YIELD-FACTOR MODEL OF INTEREST RATES DARRELLDUFFIE Graduate School ofBusine.ss, Stanford University RLJIK A N ‘ First Boston Corprution, New Ynrk This paper presents a consistent and arbitrage-free multifactor model of the term structure of interest rates in which yields at selected fixed maturities follow a parametric multivariate Markov diffusion process with “stochastic volatility.” The yield of any zero-coupon bond is taken to be a maturity- dependent affine combination of the selected “basis” set of yields. We provide necessary and sufficient conditions on the stochastic model for this affine representation. We include numerical techniques for solving the model, as wcll as numerical techniques for calculating the prices of term-structure derivative prices. The case of jump diffusions i \ also considered. I . INTRODUCTION This paper defines and analyzes a simple multifactor model of the term structure of interest rates. The factors of the model are the yields X = (XI,Xz,.. .,X , l ) of zero-coupon bonds of n various fixed maturities, I t l , r2. . , . , t,,}.For example, one could think of the current five-year (zero-coupon) yield as a factor. The yield factors form a Markov process, to be described below, that can be thought of as a multivariate version of the single-factor model of Cox, Ingersoll, and Ross ( 1 98%). As opposed to most multifactor term