Essays in Asset Pricing: Extensions and Applications of the Recovery Theorem

Abstract

This thesis has three separate goals: to provide a methodological framework for extracting risk-neutral densities from options prices, to extend the Recovery Theorem (RT) theoretically, and to apply the RT to firm decision making practices. The first chapter introduces a new model for estimating the risk-neutral density. Current estimation techniques use a single mathematical model to interpolate option prices on two dimensions: strike price and time-to-maturity (TTM). I demonstrate that, when we vary the interpolating methodology based on which dimension we are interpolating, it allows us to better extract market information. I use B-splines with at-the-money knots for the strike price interpolation and a function that depends on the option expiration horizon for the TTM interpolation. The results of this “hybrid” interpolation technique are particularly striking when compared to the common Ait-Sahalia and Lo benchmark in an application to the Recovery Theorem. My contribution is significant because it illustrates that different risk neutral density estimation techniques will reveal different market information and risk preferences. Hence, the accuracy of the density estimation is critical. In the second chapter, I redefine the prices derived in Ross's Recovery Theorem using a multivariate Markov chain rather than a univariate one. I employ a mixture transition distribution where the proposed states depend on the level of the S&P 500 index and its options' implied volatilities. I include volatility because the transition path between states depends on the propensity of an underlying asset to vary. An asset that is highly volatile is more likely to transition to a far-away state. These higher transition probabilities should lead to higher state prices. The multivariate method improves upon the univariate RT because the latter does not include the volatility inherent in the state transition, which makes its derived prices less precise. The multivariate RT produces forecast results far superior to the univariate RT. Using quarterly forecasts for the 1996-2015 period, the out-of-sample R-square of the RT increases from around 12% to 30%. Finally, in the third chapter, I answer the question: what effect does uncertainty about the aggregate economy have on investment, holding news shocks constant? Recent empirical studies have struggled to answer this question, as times of high economic uncertainty are typically also times of bad news. This chapter proposes a new methodology to measure and separate uncertainty and news shocks in stock return data. By using option prices to adjust abnormal returns for the time-varying risk premia, it is possible to estimate the impact of uncertainty shocks on firm investment while controlling for news shocks. Using quarterly data on public firms from 1996 to 2015, we find that uncertainty shocks systematically depress investment, even after controlling for bad news. Moreover, lumpy investments reinforce the negative effect of uncertainty on investment, while better management systematically attenuates this negative effect.