Empirical asset pricing with nonlinear risk premia

TL;DR

This paper introduces a flexible continuous-time asset pricing model with nonlinear risk premia, demonstrating its superior forecasting ability for volatility indices compared to standard models.

Contribution

It develops a novel nonlinear diffusion framework that guarantees solutions under the physical measure, enabling more realistic modeling of market dynamics.

Findings

Nonlinear stochastic volatility models outperform standard models in volatility forecasting.

The framework ensures existence of solutions for complex nonlinear SDEs.

Empirical analysis shows improved predictive power for S&P 100 and VXO data.

Abstract

In this paper we introduce a simple continuous-time asset pricing framework, based on general multi-dimensional diffusion processes, that combines semi-analytic pricing with a nonlinear specification for the market price of risk. Our framework guarantees existence of weak solutions of the nonlinear SDEs under the physical measure, thus allowing to work with nonlinear models for the real world dynamics not considered in the literature so far. It emerges that the additional flexibility in the time series modelling is econometrically relevant: a nonlinear stochastic volatility diffusion model for the joint time series of the S&P 100 and the VXO implied volatility index data shows superior forecasting power over the standard specifications for implied and realized variance forecasting.