Modelling Spot Rate Process in the Russian Treasury Bills Market

Abstract

The paper deals with modelling of spot rate process in the market for government securities in transitional economy. The case of the Russian Treasury bills market is taken as an example. We use three approaches to estimation of parameters of spot rate stochastic process: AR-GARCH time series models, GMM estimates and stochastic volatility models (QML estimates and Kalman filter). The most general conclusion is that pattern of spot rate process in transitional economy can be nested in existing theoretical model of term structure of interest rates. Estimated parameters of the spot rate process indicate that the Russian market for government securities by its features is closer to the European financial markets compared to the market for US Treasury bills. This conclusion is supported by estimates of parameters of the GKO spot rate stochastic process using both the GMM and QML estimates of spot rate nonlinear models. The Cox-Ingersoll-Ross 1985 model of term structure of interest rates is the most adequate for the Russian GKO market. The behaviour of the term structure of GKO yields in 1994 through 1998 did not contradict to theoretical conclusions from the model; analytical yield curves have satisfactory accuracy of approximation of actual GKO yield curves. The spot rate stochastic process is mean-reverting, but its variance although being stochastic does not exhibit mean-reverting property (according to Kalman filter estimates). The stochastic nature of spot rate volatility origins from different responses to 'good' and 'bad' news and a proportion to current spot rate level (but less than one by one).