Quadratic Gaussian Joint Pricing Model for Stocks and Bonds: Theory and Empirical Analysis

This study proposes a joint pricing model for stocks and bonds in a noarbitrage framework. A stock price representation is obtained in a manner consistent with the quadratic Gaussian term structure model, in which the short rate is the quadratic form of the state variables. In this study, specifying the dividend as a function using the quadratic form of the state variables leads to a stock price representation that is exponential-quadratic in the state variables. We prove that the coefficients determining the stock price have to satisfy some matrix equations, including an algebraic Riccati equation. Moreover, we specify the sufficient condition in which the matrix equations do have a unique solution. In our empirical analysis using Japanese data, we obtain estimates with a good fit to the actual data. Furthermore, we estimate the risk premiums for stocks and bonds and analyze how the BOJ's unconventional monetary policy has affected these risk premiums.