Effect of correlation on bond prices in short rate models of interest rates

Abstract

Short rate models of interest rates are formulated in terms of stochastic differential equations which describe the evoution of an instantaneous interest rate, called short rate. Bonds and other interest rate derivatives are then priced by a parabolic partial differential equation. We consider two-factor models, in which also correlation between the factors enters the bond-pricing differential equation. Firstly, we study the dependence of the bond prices on the correlation in three particular short rate models. The differences and common features of the results motivate us to investigate the dependence of the solution to the bond-pricing partial differential equation on the parameter representing correlation between the factors in a general case.2010 Mathematics Subject Classification. Primary: 35K15; Secondary: 35Q80. 90Effect of correlation on bond prices in short rate models

Estimating the Domestic Short Rate in a Convergence Model of Interest Rates

“…In the second scenario, another error is introduced, which comes from neglecting the effect of correlation when computing the model bond prices. However, in light of the results from [7], we do not expect the error to be large, since the bond prices are not very sensitive to the value of the correlation ρ.…”

“…. , n are then substituted into (7) and treated as known constants in further optimization. In this way, F becomes as a function of a 1 , a 2 , σ d and r di (since a 3 = −a 2 in our model) for i = 1, 2, .…”

“…We simulate 12 maturities, ranging from 1 to 12 months and use them as an input for the calibration. In the objective function (7) we consider weights w ij = τ 2 j , following the approach used in [13], [14]. The estimation procedure given above yields very precise results, which we summarize in Tables 1 and 2.…”