We propose a new decomposition of the variance risk premium (VRP) in terms of upside and downside VRPs. These components reflect market compensation for changes in good and bad uncertainties. Empirically, we establish that the downside VRP is the main component of the VRP. We find a positive and...

Specifications of the Federal Reserve target rate that have more realistic features mitigate in-sample over-fitting and are favored in the data. Imposing a positivity constraint and discrete increments significantly increase the accuracy of model out-of-sample forecasts for the level and...

Under very general conditions, the total quadratic variation of a jump-diffusion process can be decomposed into diffusive volatility and squared jump variation. We use this result to develop a new option valuation model in which the underlying asset price exhibits volatility and jump intensity...

Expected returns vary when investors face time-varying investment opportunities. In theory, structural long-run risk models (Bansal and Yaron, 2004) and no-arbitrage affine models (Duffie, Pan, and Singleton, 2000) emphasize sources of risk that are not observable to the econometrician. We show...

Plain vanilla options have a single underlying asset and a single condition on the payoff at the expiration date. For this class of options, a well-known result of Duffie, Pan and Singleton (2000) shows how to invert the characteristic function to obtain a closed-form formula for their prices....

Cochrane and Piazzesi (2005) show that (i) lagged forward rates help predict bond returns and that (ii) modern Markovian dynamic term structure models (DTSMs) cannot match the evidence. We develop the family of Conditional Mean DTSMs where the dynamics depend on current yields and their history...

We build a model for bond yields based on a small-scale representation of an economy with secular declines in inflation, the real rate and output growth. Long-run restrictions identify nominal shocks that influence long-run inflation but do not influence the long-run real rate or output growth....

We provide results for the valuation of European style contingent claims for a large class of specifications of the underlying asset returns. Our valuation results obtain in a discrete time, infinite state-space setup using the no-arbitrage principle and an equivalent martingale measure. Our...

We document that the term structures of risk-neutral expected loss and gain uncertainty on S&P 500 returns are upward sloping on average. These shapes mainly reflect the higher premium required by investors to hedge downside risk and the belief that potential gains will increase in the long run....

Plain vanilla options have a single underlying asset and a single condition on the payoff at the expiration date. For this class of options, a well-known result of Duffie, Pan and Singleton (2000) shows how to invert the characteristic function to obtain a closed-form formula for their prices....