Shedding Light on a Dark Matter : Jump Diffusion and Option-Implied Investor Preferences

We investigate the option-implied investor preferences by comparing equilibrium option pricing models under jump-diffusion to option bounds extracted from discrete-time stochastic dominance (SD). We show that the bounds converge to two prices that define an interval comparable to the observed option bid-ask spreads for S&P 500 index options. Further, the bounds' implied distributions exhibit tail risk comparable to that of the return data and thus shed light on the dark matter of the divergence between option-implied and underlying tail risks. Moreover, the bounds can better accommodate reasonable values of the ex-dividend expected excess return than the equilibrium models' prices. We examine the relative risk aversion coefficients compatible with the boundary distributions extracted from index return data. We find that the SD-restricted range of admissible RRA values is consistent with the macro-finance studies of the equity premium puzzle and with several anomalous results that have appeared in earlier option market studies