Three essays on uncertainty premium in financial markets

Abstract

This thesis consists of three essays. The first essay studies that a fear of model misspecification with regard to an external habit persistence model brings about a endogenous time-varying uncertainty aversion. A robust agent more decreases stock investment as the volatility of consumption surplus increases than an agent without model uncertainty. Within the framework of endogenous time-varying uncertainty aversion, countercyclical model uncertainty premium and procyclical P/D ratio are produced. With the optimal portfolio strategy, both the Lucas style equilibrium asset price and the risk-free rate are derived. This model provides more plausible parameter choices to explain both the equity premium puzzle and the low risk-free rate puzzle. The second essay constructs an equilibrium model of option-implied preferences with model uncertainty. The theoretical model shows that an investor with model uncertainty has a higher level of risk aversion than an investor without model uncertainty. The detectionerror probability gives a way to estimate the option-implied uncertainty aversion. Empirical findings show that the estimated option-implied risk aversion with model uncertainty is larger than that without model uncertainty. With the higher level of uncertainty aversion, the empirical uncertainty premium shows a steeper smirk pattern across wealth, which looks very similar to the smirk pattern of implied volatility of S&P 500 index options. The third essay develops a theoretical model to examine the optimal investments in R&D. The optimal level of investment in R&D is determined by three factors: (i) the expected increase in profitability, (ii) the critical level of accumulated knowledge, and (iii) the firms’s risk tolerance. An expected increase in profitability has a positive effect on investment in R&D, and firms’s risk tolerance for the future cash-flow volatility induces to increase the R&D investment. The critical level of accumulated R&D knowledge is positi...