Essay 1, Constrained Capacity and Equilibrium Forward Premia in Electricity Markets, develops a refinement of the equilibrium electricity pricing model in Bessembinder and Lemmon (2002). The refined model explicitly accounts for constrained capacity, an important feature in electricity markets. Explicitly including a role for capacity allows the model to reproduce the price spikes observed in wholesale electricity markets. The refined model implies that the equilibrium forward premium, defined to be the forward price minus the expected spot price, is decreasing in spot price variance when the expected spot electricity price is low, but is increasing in the spot price variance when the expected spot electricity price is high. Further, the refined model implies that, ceteris paribus, the equilibrium forward premium is increasing in the ratio of the expected spot electricity price to the fixed retail price. The implications of this model are closer to reality. How does currency return volatility evolve over time and what are the properties of volatility dynamics? Is the drift of currency return volatility non-linear? What forms of non-linearities are admitted in the drift and diffusion functions? The purpose of essay 2, Estimation of Continuous-Time Models for Foreign Exchange Volatility, is to estimate a large class of volatility processes and explore these issues using weekly data on two currency pairs: U.S. dollar-British pound and Japanese Yen-U.S. dollar. The estimation approach is based on maximum-likelihood estimation that relies on closed-form density approximations (A\"it-Sahalia 1999, 2002). Based on volatility implied by currency options, the constant elasticity of variance specification provides a reasonable characterization of the variance of variance function. Extending the diffusion function beyond the CEV specification does not improve the fit of the model, regardless of the assumed form of the drift function. Further, I find that certain types of non-linearities in the drift function improve the goodness of fit statistics, though no generalizations can be made.