Nikolay Nikolaev, Goldsmiths College, University of London

Modelling Interest Rates and the Yield Curve

SVIR

Stochastic Volatility of Interest Rates

Modelling the dynamics of interest rates helps to achieve accurate valuation and trading of bond futures. The pricing of such fixed income instruments is currently of increasing importance since there is increase of treasury bonds issued by all major national banks. Our research builds upon the equilibrium approach to describing the evolution of short-term riskless interest rates with a general stochastic diffusion process (which nests several other similar processes). Furthermore, the dynamic characteristics of interest rates are made proportional to their stochastic volatility. The stochastic volatility is incorporated as a time-changing diffusion coefficient for the level of the interest rate. The log-volatility of the interest rate exhibits fast mean reversion with less persistent behaviour. The volatility however is unobserved and requires treatment by algorithms many of which typically rely on sampling.

We develop practical analytical techniques for estimation of all parameters of the stochastic volatility model of interest rates with closed-form formula. There are especially designed numerical integration filters and smoothers for exact likelihood computation and expectation maximisation with respect to all parameters. These contemporary algorithms are made to operate on different versions of the diffusion model:

- autoregressive stochastic volatility model based on the Gaussian assumption;

- heavy-tailed stochastic volatility model using the Student-t distribution;

- Markov Regime-Switching model using stochastic volatility;

- Poisson jump-diffusion model with extension for spike effects.

The developed analytical algorithms are tested empirically and show comparable but faster performance to the popular Generalised Method of Moments (GMM) and Markov Chain Monte Carlo (MCMC) with Gibbs-sampling algorithms on modelling Treasury bill rates taken at different maturities.

YCM

Yield Curve Modelling

The parameters of interest rate dynamics describe the bond maturity structure, and provide information for the shape of the yield curve from spot rates at different maturities. The yiled curve tells us how to compute the price of bonds. If the dependance of the yield on the time to maturity is predicted sufficiently well then profitable trading strategies can be formulated. The econometric task involves estimation of the parameters of the interest rate model which allows for adjustment of the market risk so as to achieve minimal discrepancy between the yield curve implied by the model, and the average curve from the available sample (obtained using governmental bonds for different maturities). The features of the term structure: discount factors (zero-coupon bonds' price), short rate, and spot rate on zero-coupon bonds (forward rate) are extracted by fitting the yield curve.

Assuming nonlinear relation between the time and spot rates, our research investigates alternative term structure approximations of the yield curve dynamics to facilitate making efficient prognosis including:

- polynomial neural networks for forecasting interest rate changes and spot rates;

- multilayer Perceptron networks for predicting interest rate spreads and interest rate levels;

- approximating function models according to the Nelson Siegel framework.

Our methodology shows empirically potential to generate forward rates that are useful predictors of future spot rates for different horizons, assesed with various criteria such as directional forecast accuracy and traduing profitability.