Simulating Term Structure of Interest Rates with Arbitrary Marginals

Decision models under uncertainty need to be feeded with scenarios of the interest rate curve. Such scenarios have to comply, as close as possible, with the empirical distribution of each rate. Simulation models of the term structure usually assume that the conjugate distribution of the interest rates is lognormal. Dynamic models, like vector auto-regression, implicitly postulate that the logarithm of the interest rates is normally distributed. Statistical analyses have, however, shown that stationary transformations (yield changes) of the interest rates are substantially leptokurtic, thus posing serious doubts on the reliability of the available models. We propose in this paper a vector autoregressive model to simulate term structure of the interest rates with arbitrary marginals. We will show that our model is able to simulate paths of the entire term structure with distributional properties very close to those found in the empirical data.