A Complete Yield Curve Description of a Markov Interest Rate Model Robert J. Elliott 1 and Rogemar S. Mamon Working Paper 2000-11 Department of Statistics and Actuarial Science University of Waterloo ABSTRACT In the interest-rate market, the forward rate f (t, T ) and the yield Y (t, T ) can be written in terms of the bond price P (t, T ). Conversely, the bond price P (t, T ) can be given in terms of the forward and yield rates. Although, these three descriptions of the yield curve are equivalent, it is not always straightforward to compute them from the short rate and express one in terms of the other. Starting from a simple but very general assumption that the short-term rate r is a function of a continuous time Markov chain, we aim to get explicit analytic solutions to these three yield curve descriptions. Using stochastic flows, the bond price P (t, T ) is derived and thus the formula for the yield rate is immediately obtained. The forward measure is introduced establishing the Unbiased Expectation Hypothesis and this remarkable result is applied to calculate the dynamics of the forward rate. Our results therefore complete a term structure characterization in the study of a Markov interest rate model. Keywords: Markov chain, semi-martingale, forward measure, expectation hypothesis 1 Department of Mathematical Sciences University of Alberta Edmonton, Alberta, Canada, T6G 2G1 1