# Higher-order dynamics in asset-pricing models with recursive preferences

Schmedders, Karl; Pohl, Walter Edward; Wilms, Ole (2015). Higher-order dynamics in asset-pricing models with recursive preferences. Swiss Finance Inst 14-68, University of Zurich.

## Abstract

This paper presents an analysis of the higher-order dynamics of key financial quantities in asset-pricing models with recursive preferences. For this purpose, we first describe a projection-based algorithm for solving such models. The method outperforms common methods like discretization and log-linearization in terms of effciency and accuracy. Our algorithm allows us to document the presence of strong nonlinear effects in the modern long-run risks models which cannot be captured by the common methods. For example, for a prominent recent calibration of a popular long-run risks model, the log-linearization approach overstates the equity premium by 100 basis points or 22.5%. The increasing complexity of state-of-the-art asset-pricing models leads to complex nonlinear equilibrium functions with considerable curvature which in turn have sizable economic implications. Therefore, these models require numerical solution methods, such as the projection methods presented in this paper, that can adequately describe the higher-
order equilibrium features.

This paper presents an analysis of the higher-order dynamics of key financial quantities in asset-pricing models with recursive preferences. For this purpose, we first describe a projection-based algorithm for solving such models. The method outperforms common methods like discretization and log-linearization in terms of effciency and accuracy. Our algorithm allows us to document the presence of strong nonlinear effects in the modern long-run risks models which cannot be captured by the common methods. For example, for a prominent recent calibration of a popular long-run risks model, the log-linearization approach overstates the equity premium by 100 basis points or 22.5%. The increasing complexity of state-of-the-art asset-pricing models leads to complex nonlinear equilibrium functions with considerable curvature which in turn have sizable economic implications. Therefore, these models require numerical solution methods, such as the projection methods presented in this paper, that can adequately describe the higher-
order equilibrium features.

Detailed statistics

Item Type: Working Paper 03 Faculty of Economics > Department of Business Administration 330 Economics English 24 November 2015 21 Dec 2015 10:50 05 Apr 2016 19:42 Swiss Finance Inst 57 http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2540586 merlin-id:12803
Permanent URL: https://doi.org/10.5167/uzh-116811