A Two-Factor Term Structure Model under GARCH Volatility

Abstract

There are several advantages of an analytical valuation model for bonds and bond options when the volatility of the short rate follows a GARCH process and is the second state variable driving the yield curve besides the short rate itself. One advantage over other stochastic volatility models of the term structure is that the time-varying volatility can be easily filtered from the observed history of interest rates. Hence parameter estimation is much easier, and so is the updating of values of bonds and bond options upon changes in volatility. Calibration of the model to the U.S. Treasury yield curve (for eight different maturities) indicates that the model does not significantly improve upon the nested one-factor model in terms of pricing a cross-section of spot bonds. The implied volatilities of options on bonds exhibit a much steeper skew when option prices are generated by the model. Thus the results indicate that the effects of random volatility of the short rate are manifested mostly in bond option prices, rather than in bond prices.