Equilibrium Asset Prices and Variance Risk Premia

Abstract

This thesis studies equilibrium asset prices and variance risk premia (VRP) with three classes of models: consumption-based (Chapter 2), production-based (Chapter 3) and demand-based (Chapter 4) asset pricing models.

In Chapter 2, we provide a complete solution to the problem of equilibrium asset pricing in a pure exchange economy with two types of heterogeneous investors having higher/lower risk aversion. Using a perturbation method, we obtain analytical approximate formulas for the optimal consumption-sharing rule, which is numerically justified to be accurate for a large risk aversion and heterogeneity. We present analytical formulas for the equilibrium pricing function, Sharpe ratio, risk-free rate, stock price and optimal trading strategies. We then analyse the properties of the equilibrium and derive some testable hypotheses, which enhance our understanding on the economics of financial markets.

In Chapter 3, we provide a production-based equilibrium model with a recursive-preferences investor, which successfully explains the equity premium puzzle with very low risk aversion, and theoretically generates the negative sign of the diffusive volatility risk premium. The empirical results show that all models can perfectly explain the equity premium puzzle, and that the stochastic volatility with contemporaneous jumps (SVCJ) model and the stochastic volatility with jumps in volatility (SVJV) model built on our cost-free production economy can well capture both the large equity and variance risk premiums only if the annualized equity premium is at or larger than 11% (e.g., the periods, 1990-1999 and 2010-2016).

Chapter 4 is the first to provide a demand-based equilibrium model of volatility trading with three kinds of traders - dealers, asset managers and leveraged funds - which complements Eraker and Wu's (2017) consumption-based equilibrium model. Our theoretical results are consistent with existing empirical observations, and two endogenous cases reach the same conclusion. Our novel model links together risk aversion, market price of the volatility risk, VRP, VIX futures price and return and futures trading activities. This allows us to test empirically the impact of the three traders' net positions on the VRP and the VIX futures return.