Affine term structure models with Garch volatility
Realdon M.
December 2025Palgrave Macmillan
Risk Management
2025#27Issue 4
Investors care about the probability density of tomorrow’s Government bond yields, which is known to exhibit Garch-type conditional heteroscedasticity, but the literature on term structure models has largely avoided this issue. This paper addresses this issue through discrete time affine term structure models (DTATSM) that predict the conditional density of daily US and Euro Government bond yields and mimic the Garch-type volatility of such yields. Yields can be homoscedastic under the risk-neutral measure Q and Garch heteroscedastic under the real measure P, so that Garch heteroscedasticity is not spanned by bond prices. Thanks to more realistic predictions of daily yields volatility, the empirical evidence from US and Euro yields favours such unspanned Garch-heteroscedastic DTATSM over popular homoscedastic DTATSM and over stochastic volatility DTATSM. This result only requires a univariate unspanned Garch volatility process that aggregates the squared shocks of all the factors driving the short rate.
Affine term structure models , Discrete time , Garch heteroscedasticity , MGarch , Stochastic volatility , Tests of forecasts of densities of yields
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Bang College of Business, KIMEP, Almaty, Kazakhstan
Bang College of Business
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