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.

Financial transaction taxes, or generally transaction costs, are salient in derivatives markets and seldom studied in equilibrium models. We study a tractable model with proportional transaction costs where agents trade a derivative with nonlinear payoffs to hedge nontraded endowments. We show that trade is sustained in an equilibrium with transaction costs only if there is sufficient heterogeneity in risk aversion. When there is trade, the equilibrium return variance increases in transaction costs. These results are driven by how mean-variance demands, hedging demands, and asymmetry of no-transaction region widths determine the equilibrium Sharpe ratio and return volatility when transaction costs change.

In an incomplete market with heterogeneous prior beliefs, we show that public information can have a substantial impact on the ex ante cost of capital, trading volume, and investor welfare. The Pareto efficient public information system is the system enjoying the maximum ex ante cost of capital and the maximum expected abnormal trading volume. Imperfect public information increases the gains-to-trade based on heterogeneously updated posterior beliefs. In an exchange economy, this leads to higher growth in the investors' certainty equivalents and, thus, a higher equilibrium interest rate, whereas the ex ante risk premium is unaffected by the informativeness of the public information system. Similar results are obtained in a production economy, but the impact on the ex ante cost of capital is dampened compared to the exchange economy due to welfare-improving reductions in real investments to smooth the investors' certainty equivalents over time.