Three essays on liquidity

Doutoramento em Gestão.

Solving non-linear stochastic models by parameterizing expectations: An application to asset pricing with production

A new algorithm called the parameterized expectations approach(PEA) for solving dynamic stochastic models under rational expectationsis developed and its advantages and disadvantages are discussed. Thisalgorithm can, in principle, approximate the true equilibrium arbitrarilywell. Also, this algorithm works from the Euler equations, so that theequilibrium does not have to be cast in the form of a planner's problem.Monte--Carlo integration and the absence of grids on the state variables,cause the computation costs not to go up exponentially when the numberof state variables or the exogenous shocks in the economy increase. \\As an application we analyze an asset pricing model with endogenousproduction. We analyze its implications for time dependence of volatilityof stock returns and the term structure of interest rates. We argue thatthis model can generate hump--shaped term structures.

Pricing in stochastic-local volatility models with default

In recent years is becoming increasingly important to handle credit risk. Credit risk is the risk associated with the possibility of bankruptcy. More precisely, if a derivative provides for a payment at cert time T but before that time the counterparty defaults, at maturity the payment cannot be effectively performed, so the owner of the contract loses it entirely or a part of it. It means that the payoff of the derivative, and consequently its price, depends on the underlying of the basic derivative and on the risk of bankruptcy of the counterparty. To value and to hedge credit risk in a consistent way, one needs to develop a quantitative model. We have studied analytical approximation formulas and numerical methods such as Monte Carlo method in order to calculate the price of a bond. We have illustrated how to obtain fast and accurate pricing approximations by expanding the drift and diffusion as a Taylor series and we have compared the second and third order approximation of the Bond and Call price with an accurate Monte Carlo simulation. We have analysed JDCEV model with constant or stochastic interest rate. We have provided numerical examples that illustrate the effectiveness and versatility of our methods. We have used Wolfram Mathematica and Matlab.

Improving the analysis of road pricing acceptability surveys by using hybrid models

Several international studies have analyzed the acceptability of road pricing schemes by means of an attitude survey in combination with the results of a stated choice experiment using both a descriptive analysis and a discrete-choice model with binary choice (?accept? or ?not accept? the toll). However, the use of hybrid discrete choice models constitutes an innovative alternative for integrating subjective attitudes and perceptions deriving from the survey of attitudes with the more objective variables from the stated choice experiment. This paper analyzes the results of applying these models to measure the acceptability of interurban road pricing among different groups of stakeholders (road freight and passenger operators, highway concessionaires, and associations of private car users) with qualitatively significant opinions on road pricing measures. Our results show that hybrid models are better suited to explaining the acceptability of a road pricing scheme by different groups of stakeholders than a separate analysis of the survey of attitudes and a discrete-choice model applied on a stated choice experiment. A particular finding was that the strong psycho-social latent variable of the perception of fairness explains the rejection or acceptance of a toll scheme by road stakeholders.

Pricing farm-level agricultural insurance: a Bayesian approach

This paper applies Hierarchical Bayesian Models to price farm-level yield insurance contracts. This methodology considers the temporal effect, the spatial dependence and spatio-temporal models. One of the major advantages of this framework is that an estimate of the premium rate is obtained directly from the posterior distribution. These methods were applied to a farm-level data set of soybean in the State of the Parana (Brazil), for the period between 1994 and 2003. The model selection was based on a posterior predictive criterion. This study improves considerably the estimation of the fair premium rates considering the small number of observations.

Spatio-temporal modeling of agricultural yield data with an application to pricing crop insurance contracts

This article presents a statistical model of agricultural yield data based on a set of hierarchical Bayesian models that allows joint modeling of temporal and spatial autocorrelation. This method captures a comprehensive range of the various uncertainties involved in predicting crop insurance premium rates as opposed to the more traditional ad hoc, two-stage methods that are typically based on independent estimation and prediction. A panel data set of county-average yield data was analyzed for 290 counties in the State of Parana (Brazil) for the period of 1990 through 2002. Posterior predictive criteria are used to evaluate different model specifications. This article provides substantial improvements in the statistical and actuarial methods often applied to the calculation of insurance premium rates. These improvements are especially relevant to situations where data are limited.

Model risk in the pricing of exotic options

The growth experimented in recent years in both the variety and volume of structured products implies that banks and other financial institutions have become increasingly exposed to model risk. In this article we focus on the model risk associated with the local volatility (LV) model and with the Variance Gamma (VG) model. The results show that the LV model performs better than the VG model in terms of its ability to match the market prices of European options. Nevertheless, both models are subject to significant pricing errors when compared with the stochastic volatility framework.

No Good Deals - No Bad Models

Faced with the problem of pricing complex contingent claims, an investor seeks to make his valuations robust to model uncertainty. We construct a notion of a model- uncertainty-induced utility function and show that model uncertainty increases the investor's eff ective risk aversion. Using the model-uncertainty-induced utility function, we extend the \No Good Deals" methodology of Cochrane and Sa a-Requejo [2000] to compute lower and upper good deal bounds in the presence of model uncertainty. We illustrate the methodology using some numerical examples.

The Inflation Bias under Calvo and Rotemberg Pricing.

New Keynesian models rely heavily on two workhorse models of nominal inertia - price contracts of random duration (Calvo, 1983) and price adjustment costs (Rotemberg, 1982) - to generate a meaningful role for monetary policy. These alternative descriptions of price stickiness are often used interchangeably since, to a first order of approximation they imply an isomorphic Phillips curve and, if the steady-state is efficient, identical objectives for the policy maker and as a result in an LQ framework, the same policy conclusions. In this paper we compute time-consistent optimal monetary policy in bench-mark New Keynesian models containing each form of price stickiness. Using global solution techniques we find that the inflation bias problem under Calvo contracts is significantly greater than under Rotemberg pricing, despite the fact that the former typically significant exhibits far greater welfare costs of inflation. The rates of inflation observed under this policy are non-trivial and suggest that the model can comfortably generate the rates of inflation at which the problematic issues highlighted in the trend inflation literature emerge, as well as the movements in trend inflation emphasized in empirical studies of the evolution of inflation. Finally, we consider the response to cost push shocks across both models and find these can also be significantly different. The choice of which form of nominal inertia to adopt is not innocuous.

Modelling dependence in a ratemaking procedure with multivariate Poisson regression models

When actuaries face with the problem of pricing an insurance contract that contains different types of coverage, such as a motor insurance or homeowner's insurance policy, they usually assume that types of claim are independent. However, this assumption may not be realistic: several studies have shown that there is a positive correlation between types of claim. Here we introduce different regression models in order to relax the independence assumption, including zero-inflated models to account for excess of zeros and overdispersion. These models have been largely ignored to multivariate Poisson date, mainly because of their computational di±culties. Bayesian inference based on MCMC helps to solve this problem (and also lets us derive, for several quantities of interest, posterior summaries to account for uncertainty). Finally, these models are applied to an automobile insurance claims database with three different types of claims. We analyse the consequences for pure and loaded premiums when the independence assumption is relaxed by using different multivariate Poisson regression models and their zero-inflated versions.

Essays in equilibrium asset pricing

This thesis consists of four essays in equilibrium asset pricing. The main topic is investors' heterogeneity: I investigates the equilibrium implications for the financial markets when investors have different attitudes toward risk. The first chapter studies why expected risk and remuneration on the aggregate market are negatively related, even if intuition and standard theory suggest a positive relation. I show that the negative trade-off can obtain in equilibrium if investors' beliefs about economic fundamentals are procyclically biased and the market Sharpe ratio is countercyclical. I verify that such conditions hold in the real markets and I find empirical support for the risk-return dynamics predicted by the model. The second chapter consists of two essays. The first essay studies how het¬erogeneity in risk preferences interacts with other sources of heterogeneity and how this affects asset prices in equilibrium. Using perceived macroeconomic un¬certainty as source of heterogeneity, the model helps to explain some patterns of financial returns, even if heterogeneity is small as suggested by survey data. The second essay determines conditions such that equilibrium prices have analytical solutions when investors have heterogeneous risk attitudes and macroeconomic fundamentals feature latent uncertainty. This approach provides additional in-sights to the previous literature where models require numerical solutions. The third chapter studies why equity claims (i.e. assets paying a single future dividend) feature premia and risk decreasing with the horizon, even if standard models imply the opposite shape. I show that labor relations helps to explain the puzzle. When workers have bargaining power to exploit partial income insurance within the firm, wages are smoother and dividends are riskier than in a standard economy. Distributional risk among workers and shareholders provides a rationale to the equity short-term risk, which leads to downward sloping term structures of premia and risk for equity claim. Résumé Cette thèse se compose de quatre essais dans l'évaluation des actifs d'équilibre. Le sujet principal est l'hétérogénéité des investisseurs: J'étudie les implications d'équilibre pour les marchés financiers où les investisseurs ont des attitudes différentes face au risque. Le première chapitre étudie pourquoi attendus risque et la rémunération sur le marché global sont liées négativement, même si l'intuition et la théorie standard suggèrent une relation positive. Je montre que le compromis négatif peut obtenir en équilibre si les croyances des investisseurs sur les fondamentaux économiques sont procyclique biaisées et le ratio de Sharpe du marché est anticyclique. Je vérifier que ces conditions sont réalisées dans les marchés réels et je trouve un appui empirique à la dynamique risque-rendement prédites par le modèle. Le deuxième chapitre se compose de deux essais. Le première essai étudie com¬ment hétérogénéité dans les préférences de risque inter agit avec d'autres sources d'hétérogénéité et comment cela affecte les prix des actifs en équilibre. Utili¬sation de l'incertitude macroéconomique perù comme source d'hétérogénéité, le modèle permet d'expliquer certaines tendances de rendements financiers, même si l'hétérogénéité est faible comme suggéré par les données d'enquête. Le deuxième essai détermine des conditions telles que les prix d'équilibre disposer de solutions analytiques lorsque les investisseurs ont des attitudes des risques hétérogènes et les fondamentaux macroéconomiques disposent d'incertitude latente. Cette approche fournit un éclairage supplémentaire à la littérature antérieure où les modèles nécessitent des solutions numériques. Le troisième chapitre étudie pourquoi les equity-claims (actifs que paient un seul dividende futur) ont les primes et le risque décroissante avec l'horizon, mme si les modèles standards impliquent la forme opposée. Je montre que les relations de travail contribue à expliquer l'énigme. Lorsque les travailleurs ont le pouvoir de négociation d'exploiter assurance revenu partiel dans l'entreprise, les salaires sont plus lisses et les dividendes sont plus risqués que dans une économie standard. Risque de répartition entre les travailleurs et les actionnaires fournit une justification à le risque à court terme, ce qui conduit à des term-structures en pente descendante des primes et des risques pour les equity-claims.

Option pricing under stochastic volatility and stochastic interest rate in the Spanish case

Among the underlying assumptions of the Black-Scholes option pricingmodel, those of a fixed volatility of the underlying asset and of aconstantshort-term riskless interest rate, cause the largest empirical biases. Onlyrecently has attention been paid to the simultaneous effects of thestochasticnature of both variables on the pricing of options. This paper has tried toestimate the effects of a stochastic volatility and a stochastic interestrate inthe Spanish option market. A discrete approach was used. Symmetricand asymmetricGARCH models were tried. The presence of in-the-mean and seasonalityeffectswas allowed. The stochastic processes of the MIBOR90, a Spanishshort-terminterest rate, from March 19, 1990 to May 31, 1994 and of the volatilityofthe returns of the most important Spanish stock index (IBEX-35) fromOctober1, 1987 to January 20, 1994, were estimated. These estimators wereused onpricing Call options on the stock index, from November 30, 1993 to May30, 1994.Hull-White and Amin-Ng pricing formulas were used. These prices werecomparedwith actual prices and with those derived from the Black-Scholesformula,trying to detect the biases reported previously in the literature. Whereasthe conditional variance of the MIBOR90 interest rate seemed to be freeofARCH effects, an asymmetric GARCH with in-the-mean and seasonalityeffectsand some evidence of persistence in variance (IEGARCH(1,2)-M-S) wasfoundto be the model that best represent the behavior of the stochasticvolatilityof the IBEX-35 stock returns. All the biases reported previously in theliterature were found. All the formulas overpriced the options inNear-the-Moneycase and underpriced the options otherwise. Furthermore, in most optiontrading, Black-Scholes overpriced the options and, because of thetime-to-maturityeffect, implied volatility computed from the Black-Scholes formula,underestimatedthe actual volatility.

A general decomposition formula for derivative prices in stochastic volatility models

We see that the price of an european call option in a stochastic volatilityframework can be decomposed in the sum of four terms, which identifythe main features of the market that affect to option prices: the expectedfuture volatility, the correlation between the volatility and the noisedriving the stock prices, the market price of volatility risk and thedifference of the expected future volatility at different times. We alsostudy some applications of this decomposition.

On the relevance of modeling volatility for pricing purposes

This paper presents a two-factor (Vasicek-CIR) model of the term structure of interest rates and develops its pricing and empirical properties. We assume that default free discount bond prices are determined by the time to maturity and two factors, the long-term interest rate and the spread. Assuming a certain process for both factors, a general bond pricing equation is derived and a closed-form expression for bond prices is obtained. Empirical evidence of the model's performance in comparisson with a double Vasicek model is presented. The main conclusion is that the modeling of the volatility in the long-term rate process can help (in a large amount) to fit the observed data can improve - in a reasonable quantity - the prediction of the future movements in the medium- and long-term interest rates. However, for shorter maturities, it is shown that the pricing errors are, basically, negligible and it is not so clear which is the best model to be used.