Risk and Return in Equity and Options Markets.

Abstract

While theory can tell us about the relationship between prices of risk in options and equity markets within the context of a specific model, what we observe in the data rarely fits any single option pricing model with perfect precision. There seems to be little consensus on a single option pricing model with superior performance above all others. The purpose of this thesis is to empirically investigate the risk-return relation in options markets directly, without resorting to the use of option pricing models based upon relative pricing of options in terms of their underlying.

Options markets provide a rich cross-section of data with which to study how investors price assets because they vary across firms, strikes and maturity. As a result, options data provides additional and complimentary information beyond the information contained in stocks. Using these facts, in this thesis I empirically investigate the risk-return relationship across stock option, index option and equity markets.

In Chapter I of the thesis I empirically show how to use options data to better estimate the cross-sectional price of market-wide volatility risk. I furthermore compare the price of volatility implicit in the cross-section of stock returns with the price implicit in the cross-section of option returns. In the same chapter I exploit the fact that options can be used to study the term structure properties of risk and return by examining the volatility risk and return tradeoff in options of different times to maturity.

In Chapter II, based upon the paper "Pricing Kernel Monotonicity and Conditional Information," co-authored with Sophie Shive and Tyler Shumway, I use data on index options and the underlying index to extract estimates of stochastic discount factors. We propose a new method for non-parametrically estimating the stochastic discount factor. Our method improves upon existing methods by aligning information sets available to investors at each time in our sample and taking these into consideration in our estimation scheme. Empirical results suggest that this may be the solution to a well known anomaly in the literature whereby non-parametric estimates of the pricing kernel tend to be non-monotonic in market returns.