Calibrating Short-Rate Models to Market-observed Inflation Rates
Haverford College. Department of Economics
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This paper looks at calibrating the volatility parameter in the Hull-White short rate model to observed CPI inflation to better estimate interest rates from 1990 to 2007. Short rate models have the attractive feature of being very simple to implement but as typically used have the weakness of ignoring all macroeconomic state variables in forecasting interest rates. Interest rate models that have been developed since have been highly complex and difficult to implement. This paper thus attempts to bridge the gap between the two paradigms of interest rate models by incorporating inflation, a macroeconomic state variable, into the parameter estimation of a short rate model. To that end, the volatility parameter of the Hull-White model was calculated directly from observed rates of inflation. This volatility parameter was then used in the estimation of the mean-reversion parameter of the same model, thus involving inflation in the estimates of the two parameters of the Hull-White model. Forecasts were then compared at various horizon levels with equivalent forecasts where the parameters were estimated on the Federal Funds rate as opposed to inflation rates, representing a more typical method of calibrating these models. In comparison there was weak evidence that the use of inflation improved forecasting estimates at the 3-year horizon, but there was no evidence at other horizon levels. Further research will be required to determine if other models could benefit from the use of inflation in parameter estimation or if short-rate models could benefit further from a forward-looking as opposed to past-looking measure of inflation.