The Term Structure of Expected Quadratic Loss and Gain
43 Pages Posted: 30 Aug 2019
Date Written: August 23, 2019
We document that the term structures of risk-neutral expected squared negative (quadratic loss) and positive (quadratic gain) returns on the S&P 500 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 Andersen et al. (2015)'s 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: (1) the inclusion of jumps; (2) disentangling the price of negative jump risk from its positive analog in the stochastic discount factor specification; (3) specifying three latent factors.
Keywords: quadratic risk premium, loss uncertainty, gain uncertainty, term structure
JEL Classification: G12
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