Methodological study demonstrates numerical quadrature approximations for nonlinear asset pricing models, highlighting new solutions for equity volatility under ARCH processes.
This paper develops a discrete state space solution method for a class of nonlinear rational expectations models. The method works by using numerical quadrature rules to approximate the integral operators that arise in stochastic intertemporal models. It is particularly useful for approximating asset pricing models and has potential applications in other problems as well. An empirical application uses the method to study the relationship between the risk premium and the conditional variability of the equity returns under ARCH endowment processes.
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Tauchen et al. (1991) studied this question.
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