Essays in asset pricing

My dissertation aims at understanding the impact of uncertainty and disagreement on asset prices. It contains three main chapters. Chapter One gives a general introduction into the topic of partial information and heterogeneous beliefs. Chapter Two explains the link between credit spreads and the heterogeneous formation of expectations in an economy where agents with different perception of economic uncertainty disagree about future cash flows of a defaultable firm. The intertemporal risk-sharing of disagreeing investors gives rise to three testable implications: First, larger belief heterogeneity increases credit spreads and their volatility. Second, it implies a higher frequency of capital structure arbitrage violations. Third, it reduces expected equity returns of low levered firms, but the link can be reversed for high levered firms. We use a data-set of firm-level differences in beliefs, credit spreads, and stock returns to empirically test these predictions. The economic and statistical significance of the intertemporal risk-sharing channel of disagreement is substantial and robust to the inclusion of control variables such as Fama and French, liquidity, and implied volatility factors. Chapter Three studies the link between market-wide uncertainty, difference of opinions and co- movement of stock returns. We show that this link plays an important role in explaining the dynamics of equilibrium volatility and correlation risk premia, the differential cross-sectional pricing of index and individual options, and the risk-return profile of several option trading strategies. We use firm-specific data on analyst forecasts and test the model predictions. We obtain the following novel results: (a) The difference of index and individual volatility risk premia is linked to a counter-cyclical common disagreement component about future earnings; (b) This common component helps to explain the differential pricing of index and individual volatility smiles in the cross-section, as well as the time-series of correlation risk premia extracted from option prices; (c) The time series of returns on straddle and dispersion option portfolios reflects a significant time-varying risk premium, which compensates investors for bearing common disagreement risk; (d) Common disagreement is priced in the cross-section of option strategy returns

The conquest of U.S. inflation: learning and robustness to model uncertainty

Previous studies have interpreted the rise and fall of U.S. inflation after World War II in terms of the Fed's changing views about the natural rate hypothesis but have left an important question unanswered. Why was the Fed so slow to implement the low-inflation policy recommended by a natural rate model even after economists had developed statistical evidence strongly in its favor? Our answer features model uncertainty. Each period a central bank sets the systematic part of the inflation rate in light of updated probabilities that it assigns to three competing models of the Phillips curve. Cautious behavior induced by model uncertainty can explain why the central bank presided over the inflation of the 1970s even after the data had convinced it to place much the highest probability on the natural rate model. JEL Classification: E31, E58, E65anticipated utility, Bayes' law, natural unemployment rate, Phillips curve, Robustness

On the Mathematical Theory of Ensemble (Linear-Gaussian) Kalman-Bucy Filtering

The purpose of this review is to present a comprehensive overview of the theory of ensemble Kalman-Bucy filtering for linear-Gaussian signal models. We present a system of equations that describe the flow of individual particles and the flow of the sample covariance and the sample mean in continuous-time ensemble filtering. We consider these equations and their characteristics in a number of popular ensemble Kalman filtering variants. Given these equations, we study their asymptotic convergence to the optimal Bayesian filter. We also study in detail some non-asymptotic time-uniform fluctuation, stability, and contraction results on the sample covariance and sample mean (or sample error track). We focus on testable signal/observation model conditions, and we accommodate fully unstable (latent) signal models. We discuss the relevance and importance of these results in characterising the filter's behaviour, e.g. it's signal tracking performance, and we contrast these results with those in classical studies of stability in Kalman-Bucy filtering. We provide intuition for how these results extend to nonlinear signal models and comment on their consequence on some typical filter behaviours seen in practice, e.g. catastrophic divergence

Applications of robust optimal control to decision making in the presence of uncertainty

This thesis is concerned with robustness of decision making in financial economics. Feedback control models developed in engineering are applied to three separate though linked problems in order to examine the role and impact of robustness in the creation and application of decision rules. Three problems are examined using robust optimal control techniques to evaluate the impact of robustness and stability in financial economic models. The first problem examines the use of linear models of robust optimal control in the pricing of castastrophe based derivatives and finds its relative performance to be superior to the popular jump diffusion and stochastic volatility models in the pricing of these emerging instruments. The novelty of the approach arises from the examination of the impact of robustness and stability of the pricing solution. The second problem involves robustness and stability of hedging. An alternative method of creating hedging rules is developed. The method is based on robust control Lyapunov functions that are simple, robust and stable in operation, yet in practice are not so conservative that they eliminate all trading gains. The third problem involves the development of robust control policies for managing risk, using non-linear robust optimal control techniques to provide clear evidence of superior performance of robust models when compared with existing VAR and EVT approaches to risk management. The novelty in the approach arises from the development of a simple and powerful risk management metric

Ambiguity and information processing in a model of intermediary asset pricing

This paper incorporates ambiguity and information processing constraints into a model of intermediary asset pricing. Financial intermediaries are assumed to possess greater information processing capacity. Households purchase this capacity, and then delegate their investment decisions to intermediaries. As in He and Krishnamurthy (2012), the delegation contract is constrained by a moral hazard problem, which gives rise to a minimum capital requirement. Both households and intermediaries have a preference for robustness, reflecting ambiguity about asset returns (Hansen and Sargent (2008)). We show that ambiguity aversion tightens the capital constraint, and amplifies its effects. Detection error probabilities are used to discipline the degree of ambiguity aversion. The model can explain both the unconditional moments of asset returns and their state dependence, even with DEPs in excess of 20%.https://papers.ssrn.com/sol3/papers.cfm?abstract_id=3386888First author draf

Mathematics of Quantitative Finance

The workshop on Mathematics of Quantitative Finance, organised at the Mathematisches Forschungsinstitut Oberwolfach from 26 February to 4 March 2017, focused on cutting edge areas of mathematical finance, with an emphasis on the applicability of the new techniques and models presented by the participants