Abstract
I study the joint dynamics of consumption and asset returns. In the first chapter, I estimate a DSGE model of a production economy to explore what features in this class of models can account for the long-run risk and stochastic volatility I observe in the data on consumption growth and equity returns. In the asset-pricing literature, there has been a proliferation of endowment economy models that exogenously contain a persistent shock to the average growth rate, known as long-run risk, and a persistent shock to the volatility, known as stochastic volatility, of consumption and dividend growth. Once calibrated, these models successfully account for several well-known asset-pricing puzzles. I use Quasi-Maximum Likelihood and the Kalman filter to estimate the long-run risk and stochastic volatility present in consumption growth and equity returns data. I show that the persistence of the long-run risk and stochastic volatility in the data is significantly lower than has previously been assumed by the literature.
Next, I use Indirect Inference to estimate a production economy model. The key features of my model are long-run risk and stochastic volatility in the exogenous process for aggregate productivity growth, as well as rare disaster events that destroy a fraction of the capital stock and occur with a probability that varies persistently over time. I show that the estimated model, which delivers empirically plausible long-run risk and stochastic volatility in consumption growth and equity returns, is not able to resolve well-known asset pricing puzzles. I provide evidence that improving the model’s asset pricing implications comes at the expense of delivering empirically plausible consumption dynamics. Finally, including both long-run productivity risk and disaster risk together improves the model’s ability to account for asset price and business cycle quantity moments simultaneously.
In the second chapter of my dissertation, I use the estimated DSGE model of a production economy from Chapter 1 to analyze options prices. I price five European call options, each with the previous chapter's equity asset as the underlying asset. The options all have a three month maturity and range in strike price from ten percent below the spot price to ten percent above it. I show that the price of the ITM options are increasing in today's level of capital, while the price of the ATM and OTM options are decreasing in the current capital stock. I show that the inclusion of long-run productivity risk has a significant impact on the slope of these pricing functions, while the inclusion of disaster risk in the model does not. Next, I simulate this economy and show that it produces an implied volatility smirk. I propose a measure for the average level of implied volatility skew. Finally, I show how eliminating long-run productivity risk and rare disaster risk from the model affect this measure.
