The Term Structures of Expected Loss and Gain Uncertainty

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. The term structures exhibit substantial time-series variation with large negative slopes during crisis periods. Through the lens of a flexible Jump-Diffusion framework, we evaluate the ability of existing reduced-form option pricing models to replicate these term structures. We stress that three ingredients are particularly important: (i) the inclusion of jumps; (ii) disentangling the price of negative jump risk from its positive analog in the stochastic discount factor specification; and (iii) specifying three latent factors.