Good Deals and compatible modification of risk and pricing rule: a regulatory treatment.

This work studies Good Deals in a scenario in which a fir uses decision-making tools based on a coherent risk measure, and in which the market prices are determined with a sub-linear pricing rule. The most important observation of this work is that the existence of a Good Deal is equivalent to the incompatibility between the pricing rule and the risk measure. In this paper, we look into this situation from a regulatory point of view to rule out Good Deals with the purpose of stabilizing financia markets. We propose some practical ways of modifying a risk measure so a regulator can set appropriate levels of capital requirements for a financia institution.Coherent risk measures; Princing rule; Good deal; Compatibility;

Hedging and pricing in imperfect markets under non-convexity

This paper proposes a robust approach to hedging and pricing in the presence of market imperfections such as market incompleteness and frictions. The generality of this framework allows us to conduct an in-depth theoretical analysis of hedging strategies for a wide family of risk measures and pricing rules, which are possibly non-convex. The practical implications of our proposed theoretical approach are illustrated with an application on hedging economic risk

On some aspects of coherent risk measures and their applications

Le sujet principal de cette thèse porte sur les mesures de risque. L'objectif général est d'investiguer certains aspects des mesures de risque dans les applications financières. Le cadre théorique de ce travail est celui des mesures cohérentes de risque telle que définie dans Artzner et al (1999). Mais ce n'est pas la seule classe de mesure du risque que nous étudions. Par exemple, nous étudions aussi quelques aspects des "statistiques naturelles de risque" (en anglais natural risk statistics) Kou et al (2006) et des mesures convexes du risque Follmer and Schied(2002). Les contributions principales de cette thèse peuvent être regroupées selon trois axes: allocation de capital, évaluation des risques et capital requis et solvabilité. Dans le chapitre 2 nous caractérisons les mesures de risque avec la propriété de Lebesgue sur l'ensemble des processus bornés càdlàg (continu à droite, limité à gauche). Cette caractérisation nous permet de présenter deux applications dans l'évaluation des risques et l'allocation de capital. Dans le chapitre 3, nous étendons la notion de statistiques naturelles de risque à l'espace des suites infinies. Cette généralisation nous permet de construire de façon cohérente des mesures de risque pour des bases de données de n'importe quelle taille. Dans le chapitre 4, nous discutons le concept de "bonnes affaires" (en anglais Good Deals), pour notamment caractériser les situations du marché où ces positions pathologiques sont présentes. Finalement, dans le chapitre 5, nous essayons de relier les trois chapitres en étendant la définition de "bonnes affaires" dans un cadre plus large qui comprendrait les mesures de risque analysées dans les chapitres 2 et 3.The aim of this thesis is to study several aspects of risk measures particularly in the context of financial applications. The primary framework that we use is that of coherent risk measures as defined in Artzner et al (1999). But this is not the only class of risk measures that we study here. We also investigate the concepts of natural risk statistics Kou et al (2006) and convex risk measure Follmer/ and Schied (2002). The main contributions of this Thesis can be classified in three main axes: Capital allocation, risk measurement and capital requirement and solvency. In chapter 2, we characterize risk measures with the Lebesgue property on bounded càdlàg processes. This allows to present two applications in risk assessment and capital allocation. In chapter 3, we extend the concept of natural risk statistics to the space of infinite sequences. This has been done in order to introduce a consistent way of constructing risk measures for data bases of any size. In chapter 4, we discuss the concept of Good Deals and how to deal with a situation where these pathological positions are present in the market. Finally, in chapter 5, we try to relate all three chapters by extending the definition of Good Deals to a larger set of risk measures that somehow includes the discussions in chapters 2 and 3

HEDGING AND PRICING IN INCOMPLETE MARKETS: THEORY AND APPLICATIONS

This thesis consists of three essays in financial econometrics. In the first part of the thesis, motivated by different applications of hedging methods in the literature, we propose a general theoretical framework for hedging and pricing. First, we review briefly different strands of literature on hedging which have been developed in various fields such as finance, economics, operations research and mathematics, and then try to come up with a tractable way for hedging and pricing in this paper. By introducing different market principles, we study conditions under which the hedging problem has a solution and pricing is possible. We will conduct an in-depth theoretical analysis of hedging strategies with shortfall risks as well as the spectral risk measures, in particular those associated with Choquet expected utility. We show that asymmetric information results in incorrect risk assessment and pricing. In the second part of the thesis, we will apply our results in the first part to construct an economic risk hedge. We also introduce a general method to estimate the stochastic discount factors associated with different risk measures and different financial models. The third part of the thesis modifies the speculative storage model by embedding staggered price features into the structural model of Deaton and Laroque (1996). In an attempt to replicate the stylized facts of observed commodity price dynamics, we add an additional source of intertemporal linkage to Deaton and Laroque (1996), namely speculation in intermediate-good inventories. The introduction of this type of friction into the model is motivated by its ability to increase price stickiness which gives rise to an increased persistence in the first and higher conditional moments of commodity prices. By incorporating intermediate risk neutral speculators and a final bundler with a staggered pricing rule in the spirit of Calvo (1983) into the storage model, we are able to capture a high degree of serial correlation and conditional heteroskedasticity, which are observed in actual data. The structural parameters of both Deaton and Laroque (1996) and our modified models are estimated using actual prices for 8 agricultural commodities. Simulated data are then employed to assess the effects of our staggered price approach on the time-series properties of commodity prices. Our results lend empirical support to the possibility of staggered prices

Good Deals and compatible modification of risk and pricing rule: a regulatory treatment

This work studies Good Deals in a scenario in which a fir uses decision-making tools based on a coherent risk measure, and in which the market prices are determined with a sub-linear pricing rule. The most important observation of this work is that the existence of a Good Deal is equivalent to the incompatibility between the pricing rule and the risk measure. In this paper, we look into this situation from a regulatory point of view to rule out Good Deals with the purpose of stabilizing financia markets. We propose some practical ways of modifying a risk measure so a regulator can set appropriate levels of capital requirements for a financia institution.This work is partially supported by University of Montreal (bourse de mobilité), the Spanish Government (Grant ECO2009-14457-C04)Publicad