Dynamic hedging with stocastic differential utility

In this paper we study the dynamic hedging problem using three different utility specifications: stochastic differential utility, terminal wealth utility, and we propose a particular utility transformation connecting both previous approaches. In all cases, we assume Markovian prices. Stochastic differential utility, SDU, impacts the pure hedging demand ambiguously, but decreases the pure speculative demand, because risk aversion increases. We also show that consumption decision is, in some sense, independent of hedging decision. With terminal wealth utility, we derive a general and compact hedging formula, which nests as special all cases studied in Duffie and Jackson (1990). We then show how to obtain their formulas. With the third approach we find a compact formula for hedging, which makes the second-type utility framework a particular case, and show that the pure hedging demand is not impacted by this specification. In addition, with CRRA- and CARA-type utilities, the risk aversion increases and, consequently the pure speculative demand decreases. If futures price are martingales, then the transformation plays no role in determining the hedging allocation. We also derive the relevant Bellman equation for each case, using semigroup techniques.

A Structural Analysis of the Health Expenditures and Portfolio Choices of Retired Agents

Richer and healthier agents tend to hold riskier portfolios and spend proportionally less on health expenditures. Potential explanations include health and wealth effects on preferences, expected longevity or disposable total wealth. Using HRS data, we perform a structural estimation of a dynamic model of consumption, portfolio and health expenditure choices with recursive utility, as well as health-dependent income and mortality risk. Our estimates of the deep parameters highlight the importance of health capital, mortality risk control, convex health and mortality adjustment costs and binding liquidity constraints to rationalize the stylized facts. They also provide new perspectives on expected longevity and on the values of life and health.

The value of useless information

There are many situations in which individuals have a choice of whether or notto observe eventual outcomes. In these instances, individuals often prefer to remainignorant. These contexts are outside the scope of analysis of the standard vonNeumann-Morgenstern (vNM) expected utility model, which does not distinguishbetween lotteries for which the agent sees the final outcome and those for which hedoes not. I develop a simple model that admits preferences for making an observationor for remaining in doubt. I then use this model to analyze the connectionbetween preferences of this nature and risk-attitude. This framework accommodatesa wide array of behavioral patterns that violate the vNM model, and thatmay not seem related, prima facie. For instance, it admits self-handicapping, inwhich an agent chooses to impair his own performance. It also accommodatesa status quo bias without having recourse to framing effects, or to an explicitdefinition of reference points. In a political economy context, voters have strictincentives to shield themselves from information. In settings with other-regardingpreferences, this model predicts observed behavior that seems inconsistent witheither altruism or self-interested behavior.

Measuring time-varying economic fears with consumption-based stochastic discount factors

This paper analyzes empirically the volatility of consumption-based stochastic discount factors as a measure of implicit economic fears by studying its relationship with future economic and stock market cycles. Time-varying economic fears seem to be well captured by the volatility of stochastic discount factors. In particular, the volatility of recursive utility-based stochastic discount factor with contemporaneous growth explains between 9 and 34 percent of future changes in industrial production at short and long horizons respectively. They also explain ex-ante uncertainty and risk aversion. However, future stock market cycles are better explained by a similar stochastic discount factor with long-run consumption growth. This specification of the stochastic discount factor presents higher volatility and lower pricing errors than the specification with contemporaneous consumption growth.

Three essays in financial economics: asset pricing, optimal portfolio selection and financial integration

Executive Summary The unifying theme of this thesis is the pursuit of a satisfactory ways to quantify the riskureward trade-off in financial economics. First in the context of a general asset pricing model, then across models and finally across country borders. The guiding principle in that pursuit was to seek innovative solutions by combining ideas from different fields in economics and broad scientific research. For example, in the first part of this thesis we sought a fruitful application of strong existence results in utility theory to topics in asset pricing. In the second part we implement an idea from the field of fuzzy set theory to the optimal portfolio selection problem, while the third part of this thesis is to the best of our knowledge, the first empirical application of some general results in asset pricing in incomplete markets to the important topic of measurement of financial integration. While the first two parts of this thesis effectively combine well-known ways to quantify the risk-reward trade-offs the third one can be viewed as an empirical verification of the usefulness of the so-called "good deal bounds" theory in designing risk-sensitive pricing bounds. Chapter 1 develops a discrete-time asset pricing model, based on a novel ordinally equivalent representation of recursive utility. To the best of our knowledge, we are the first to use a member of a novel class of recursive utility generators to construct a representative agent model to address some long-lasting issues in asset pricing. Applying strong representation results allows us to show that the model features countercyclical risk premia, for both consumption and financial risk, together with low and procyclical risk free rate. As the recursive utility used nests as a special case the well-known time-state separable utility, all results nest the corresponding ones from the standard model and thus shed light on its well-known shortcomings. The empirical investigation to support these theoretical results, however, showed that as long as one resorts to econometric methods based on approximating conditional moments with unconditional ones, it is not possible to distinguish the model we propose from the standard one. Chapter 2 is a join work with Sergei Sontchik. There we provide theoretical and empirical motivation for aggregation of performance measures. The main idea is that as it makes sense to apply several performance measures ex-post, it also makes sense to base optimal portfolio selection on ex-ante maximization of as many possible performance measures as desired. We thus offer a concrete algorithm for optimal portfolio selection via ex-ante optimization over different horizons of several risk-return trade-offs simultaneously. An empirical application of that algorithm, using seven popular performance measures, suggests that realized returns feature better distributional characteristics relative to those of realized returns from portfolio strategies optimal with respect to single performance measures. When comparing the distributions of realized returns we used two partial risk-reward orderings first and second order stochastic dominance. We first used the Kolmogorov Smirnov test to determine if the two distributions are indeed different, which combined with a visual inspection allowed us to demonstrate that the way we propose to aggregate performance measures leads to portfolio realized returns that first order stochastically dominate the ones that result from optimization only with respect to, for example, Treynor ratio and Jensen's alpha. We checked for second order stochastic dominance via point wise comparison of the so-called absolute Lorenz curve, or the sequence of expected shortfalls for a range of quantiles. As soon as the plot of the absolute Lorenz curve for the aggregated performance measures was above the one corresponding to each individual measure, we were tempted to conclude that the algorithm we propose leads to portfolio returns distribution that second order stochastically dominates virtually all performance measures considered. Chapter 3 proposes a measure of financial integration, based on recent advances in asset pricing in incomplete markets. Given a base market (a set of traded assets) and an index of another market, we propose to measure financial integration through time by the size of the spread between the pricing bounds of the market index, relative to the base market. The bigger the spread around country index A, viewed from market B, the less integrated markets A and B are. We investigate the presence of structural breaks in the size of the spread for EMU member country indices before and after the introduction of the Euro. We find evidence that both the level and the volatility of our financial integration measure increased after the introduction of the Euro. That counterintuitive result suggests the presence of an inherent weakness in the attempt to measure financial integration independently of economic fundamentals. Nevertheless, the results about the bounds on the risk free rate appear plausible from the view point of existing economic theory about the impact of integration on interest rates.

Empirical Assessment of an Intertemporal Option Pricing Model with Latent variables

This paper assesses the empirical performance of an intertemporal option pricing model with latent variables which generalizes the Hull-White stochastic volatility formula. Using this generalized formula in an ad-hoc fashion to extract two implicit parameters and forecast next day S&P 500 option prices, we obtain similar pricing errors than with implied volatility alone as in the Hull-White case. When we specialize this model to an equilibrium recursive utility model, we show through simulations that option prices are more informative than stock prices about the structural parameters of the model. We also show that a simple method of moments with a panel of option prices provides good estimates of the parameters of the model. This lays the ground for an empirical assessment of this equilibrium model with S&P 500 option prices in terms of pricing errors.

Risk Aversion, Intertemporal Substitution, and Option Pricing

This paper develops a general stochastic framework and an equilibrium asset pricing model that make clear how attitudes towards intertemporal substitution and risk matter for option pricing. In particular, we show under which statistical conditions option pricing formulas are not preference-free, in other words, when preferences are not hidden in the stock and bond prices as they are in the standard Black and Scholes (BS) or Hull and White (HW) pricing formulas. The dependence of option prices on preference parameters comes from several instantaneous causality effects such as the so-called leverage effect. We also emphasize that the most standard asset pricing models (CAPM for the stock and BS or HW preference-free option pricing) are valid under the same stochastic setting (typically the absence of leverage effect), regardless of preference parameter values. Even though we propose a general non-preference-free option pricing formula, we always keep in mind that the BS formula is dominant both as a theoretical reference model and as a tool for practitioners. Another contribution of the paper is to characterize why the BS formula is such a benchmark. We show that, as soon as we are ready to accept a basic property of option prices, namely their homogeneity of degree one with respect to the pair formed by the underlying stock price and the strike price, the necessary statistical hypotheses for homogeneity provide BS-shaped option prices in equilibrium. This BS-shaped option-pricing formula allows us to derive interesting characterizations of the volatility smile, that is, the pattern of BS implicit volatilities as a function of the option moneyness. First, the asymmetry of the smile is shown to be equivalent to a particular form of asymmetry of the equivalent martingale measure. Second, this asymmetry appears precisely when there is either a premium on an instantaneous interest rate risk or on a generalized leverage effect or both, in other words, whenever the option pricing formula is not preference-free. Therefore, the main conclusion of our analysis for practitioners should be that an asymmetric smile is indicative of the relevance of preference parameters to price options.

A consumption CAPM with a reference level

We study an intertemporal asset pricing model in which a representative consumer maximizes expected utility derived from both the ratio of his consumption to some reference level and this level itself. If the reference consumption level is assumed to be determined by past consumption levels, the model generalizes the usual habit formation specifications. When the reference level growth rate is made dependent on the market portfolio return and on past consumption growth, the model mixes a consumption CAPM with habit formation together with the CAPM. It therefore provides, in an expected utility framework, a generalization of the non-expected recursive utility model of Epstein and Zin (1989). When we estimate this specification with aggregate per capita consumption, we obtain economically plausible values of the preference parameters, in contrast with the habit formation or the Epstein-Zin cases taken separately. All tests performed with various preference specifications confirm that the reference level enters significantly in the pricing kernel.

Stress at work among electric utility workers

In the last decades there was an increase in stress at work and its effects on workers' health. These issues are still little studied in the electric utility sector. This study aims to evaluate factors associated with stress at work and to verify its associations with health status among workers of an electric company in São Paulo State, Brazil. A cross-sectional study was conducted with 474 subjects (87.5% of the eligible workers). Data were collected using self-reported questionnaires. A descriptive analysis, a multiple linear hierarchical regression analysis and a correlation analysis were performed. The majority of participants were males (91.1%) and the mean age was 37.5 yr. The mean score of stress level was 2.3 points (scale ranging from 1.0 to 5.0). Hierarchical multiple analyses showed that: regular practice of physical activities (p=0.025) and individual monthly income (p=0.002) were inversely associated with stress level; BMI was marginally associated with the stress level (p=0.074). The demographic characteristics were not associated with stress. Stress at work was significantly associated with physical and mental health status (p<0.001). To improve health of electric utility workers, actions are suggested to decrease stress by remuneration and an appropriate practice of physical activity aiming reduction of BMI

Stress at Work among Electric Utility Workers

In the last decades there was an increase in stress at work and its effects on workers' health. These issues are still little studied in the electric utility sector. This study aims to evaluate factors associated with stress at work and to verify its associations with health status among workers of an electric company in Sao Paulo State, Brazil. A cross-sectional study was conducted with 474 subjects (87.5% of the eligible workers). Data were collected using self-reported questionnaires. A descriptive analysis, a multiple linear hierarchical regression analysis and a correlation analysis were performed. The majority of participants were males (91.1%) and the mean age was 37.5 yr. The mean score of stress level was 2.3 points (scale ranging from 1.0 to 5.0). Hierarchical multiple analyses showed that: regular practice of physical activities (p=0.025) and individual monthly income (p=0.002) were inversely associated with stress level; BMI was marginally associated with the stress level (p=0.074). The demographic characteristics were not associated with stress. Stress at work was significantly associated with physical and mental health status (p<0.001). To improve health of electric utility workers, actions are suggested to decrease stress by remuneration and an appropriate practice of physical activity aiming reduction of BMI.

Utility of Quantitative Ultrasound of the Calcaneus in Diagnosing Osteoporosis in Spinal Cord Injury Patients

Bittar CK, Cliquet A Jr, dos Santos Floter M: Utility of quantitative ultrasound of the calcaneus in diagnosing osteoporosis in spinal cord injury patients. Am J Phys Med Rehabil 2011;90:477-481. Objective: The aim of this study was to assess the utility of quantitative ultrasound of the calcaneus in diagnosing osteoporosis in spinal cord injury patients in a Brazilian Teaching Hospital. Design: This is a diagnostic test criterion standard comparison study. Between January 2008 and October 2009, the bone density of 15 spinal cord injury patients was assessed for analysis before beginning rehabilitation using muscle stimulation. The bone density was assessed using bone densitometry examination (DEXA) and ultrasound examination of the calcaneus (QUS). The measurements acquired using QUS and DEXA were compared between patients with spinal cord injury and a control group of ten healthy individuals. Results: The T-score values for femoral neck using DEXA (P < 0.0022) and those using QUS of the calcaneus (P < 0.0005) differed significantly between the groups, and the means in the normal subjects were higher than those in spinal cord injury patients who would receive electrical stimulation. In spinal cord injury patients, the significant differences were found between the QUS T-score for calcaneus and the DEXA scores for the lumbar spine and femoral neck. Conclusions: Because of the low level of mechanical stress on the calcaneus, the results of the QUS could not be correlated with the DEXA results for diagnosing osteoporosis. Therefore, QUS seems to be not a good choice for diagnosis and follow-up.

Recursive linear estimation for general discrete-time descriptor systems

This paper considers the optimal linear estimates recursion problem for discrete-time linear systems in its more general formulation. The system is allowed to be in descriptor form, rectangular, time-variant, and with the dynamical and measurement noises correlated. We propose a new expression for the filter recursive equations which presents an interesting simple and symmetric structure. Convergence of the associated Riccati recursion and stability properties of the steady-state filter are provided. (C) 2010 Elsevier Ltd. All rights reserved.

An Array Recursive Least-Squares Algorithm With Generic Nonfading Regularization Matrix

We present a novel array RLS algorithm with forgetting factor that circumvents the problem of fading regularization, inherent to the standard exponentially-weighted RLS, by allowing for time-varying regularization matrices with generic structure. Simulations in finite precision show the algorithm`s superiority as compared to alternative algorithms in the context of adaptive beamforming.