An Interest Rate Model with Upper and Lower Bounds

We propose a new interest rate dynamics model where the interest rates fluctuate in a bounded region. The model is characterised by five parameters which are sufficiently flexible to reflect the prediction of the future interest rates distribution. The interest rate converges in law to a Beta distribution and has transition probabilities which are represented by a series of Jacobi polynomials. We derive the moment evaluation formula of the interest rate. We also derive the arbitrage free pure discount bond price formula by a weighted series of Jacobi polynomials. Furthermore we give simple lower and upper bounds for the arbitrage free discount bond price which are tight for the narrow interest rates region case. Finally we show that the numerical evaluation procedure converges to the exact value in the limit and evaluate the accuracy of the approximation formulas for the discount bond prices.