Standard Gaussian term structure models impose the Markov property: the conditional mean is a function of the risk factors. We relax this assumption and consider models where yields are linear in the conditional mean (but not in the risk factors). To illustrate, yields should span expected inflation but not inflation. Second, expected and surprise yield changes can have opposite contemporaneous effects on expected inflation. Third, the survey forecasts and inflation rate can both be in the state. These three features are inconsistent with the Markov assumption. These effects matter empirically in the USA and in Canada.

Many studies have documented that daily realized volatility estimates based on intraday returns provide volatility forecasts that are superior to forecasts constructed from daily returns only. We investigate whether these forecasting improvements translate into economic value added. To do so, we develop a new class of affine discrete-time option valuation models that use daily returns as well as realized volatility. We derive convenient closed-form option valuation formulas, and we assess the option valuation properties using Standard & Poor’s (S&P) 500 return and option data. We find that realized volatility reduces the pricing errors of the benchmark model significantly across moneyness, maturity, and volatility levels.

Structural or no-arbitrage asset-pricing models emphasize risk factors that cannot be observed directly. We show that the term structure of risk implicit in option prices can reveal these risk factors. Empirically, the variance term structure reveals two predictors of the bond premium, the equity premium, and the variance premium, jointly. Similarly, the term structures of skewness and kurtosis measures also reveal risk factors, but these are subsumed in the predictive content of the variance. The predicted premium is countercyclical and robust to the inclusion of known returns predictors.