Speculations in option markets enhance allocation efficiency with heterogeneous beliefs and learning

Many studies investigate the impact of heterogeneous beliefs in the first moment, while very few in the second moment. This is partially due to continuous-time setup which makes it difficult to incorporate heterogeneous beliefs in the second moment. In a two-period exponential-normal model with Bayesian learning, I demonstrate that heterogeneous prior variances give rise to the economic value of option markets. Investors speculate in option market and public information improves allocation efficiency of markets only when there is heterogeneity in prior variances. Heterogeneity in mean is neither a necessary nor a sufficient condition for generating speculations in option markets. With heterogeneous beliefs, options are non-redundant assets which can facilitate side-betting and enable investors to take advantage of the disagreements and the differences in confidence. This fact leads to a higher growth rate in the investors' certainty equivalents and, thus, a higher equilibrium interest rate. Furthermore, option exhibits a unique feature of enabling signal precision to affect the ex ante risk premium of underlying asset, which quadratic derivative and stock do not have.