Essays in discrete time asset pricing

Most discrete time literature uses the beta that results from a regression of an asset\u27s simple returns on various factors to quantify risk. The departing point for this thesis is the consistent use of log-returns. When log-returns are considered, the relevant measure of systematic risk becomes the log-return beta. A statistical transformation, the Cumulant Generating Function, captures risk premia. Distributional CAPM, directly connects risk premia to return distributions. In the second chapter, I develop discrete time asset pricing for affine economies. I define a discrete time affine process as one where the conditional cumulant generating function is affine in the current state. Equivalently conditional cumulants are affine. Based on this definition, I derive closed-form prices for bonds, and bond options. Given the newly developed definition of a discrete-time affine process, I extend the square-root diffusion without violating its affine character. In the third chapter, I define the π-process, a non-trivial generalization of the square-root diffusion in discrete-time. The conditional distribution of a square-root diffusion, a scaled non-central chi-square, depends on the state through its non-centrality parameter: q. In a π-process, both the non-centrality, and, the degrees of freedom ν become affine functions of the current state. This definition creates a multifactor process that can be used to model conditional heteroscedasticity beyond the traditional GARCH paradigm. The additional benefit is that financial assets and derivatives are easily priced in discrete time. In the fourth chapter, I quantify the effect of an increased flow of information on fixed income assets. Flow of information is modeled as the discreteness τ in a discrete-time economy. I model two otherwise identical economies that differ only with respect to the speed at which information is incorporated into the production process. The “old” economy can only incorporate new information every quarter while the “new” economy incorporates shocks as fast as every week. Both economies are calibrated with US data. I find an increased volatility for bond prices in the “new” economy that results in substantially increased option prices