Price Dynamics in Market with Heterogeneous Investment Horizons and Boundedly Rational Traders

This paper studies the effects of multiple investment horizons and investors' bounded rationality on the price dynamics. We consider a pure exchange economy with one risky asset, populated with agents maximizing CRRA-type expected utility of wealth over discrete investment periods. An investor's demand for the risky asset may depend on the historical returns, so that our model encompasses a wide range of behaviorist patterns. The necessary conditions, under which the risky return can be a stationary iid process, are established. The compatibility of these conditions with different types of demand functions in the heterogeneous agents' framework are explored. We find that conditional volatility of returns cannot be constant in many generic situations, especially if agents with different investment horizons operate on the market. In the latter case the return process can display conditional heteroscedasticity, even if all investors are so-called "fundamentalists" and their demand for the risky asset is subject to exogenous iid shocks. We show that the heterogeneity of investment horizons can be a possible explanation of different stylized patterns in stock returns, in particular, mean-reversion and volatility clustering.Asset pricing, heterogeneous agents, multiple investment scales, volatility clustering.

Pricing and Hedging Options in Incomplete Markets: Idiosyncratic Risk, Systematic Risk and Stochastic Volatility

Starting from the European option valuation framework of Chauveau & Gatfaoui (2002), we establish the link with stochastic volatility models. And, we propose both a new vision and a general framework for valuing European options in the light of systematic and idiosyncratic risks affecting risky assets in the financial market. Therefore, we account for the well-known volatility smile in the light of the literature addressing the determinants of the smile effect among which stochastic volatility and market risk. We further discuss briefly the hedging of European options along with the local risk minimization principle. Specifically, we attempt to find a strategy, which dominates the usual partial hedging technique often imposed by market’s incompleteness.Call pricing, idiosyncratic risk, incomplete market, stochastic volatility, systematic risk.

Subjective risk and disappointment

URL des Documents de travail : http://centredeconomiesorbonne.univ-paris1.fr/bandeau-haut/documents-de-travail/Documents de travail du Centre d'Economie de la Sorbonne 2012.63 - ISSN : 1955-611X - Version révisée : mars 2013If an investor does care for utilities -and not for monetary outcomes- stochastic dominances should be expressed in terms of utility units ("utils"). If so, any "rational" investor may be characterized by an elementary utility function -called canonical utility function- which is such that the partial weak order induced by stochastic dominance over utils is as "close" to the weak order of preferences as possible. As a consequence, the random utilities of the available prospects do not violate the second-order stochastic dominance property. Substituting utils for monetary units leads to substitute "subjective" risk for "objective" risk à la Rothschild and Stiglitz (1970). A weakened independence axiom may them be set over comparable prospects, i.e. those which exhibit the same canonical expected utility. This leads to a fully choice-based theory of disappointment. The functional is lottery-dependent (Becker and Sarin 1987). When constant marginal utility is assumed, it is but the opposite to a convex measure of risk (Föllmer and Schied 2002). It may be viewed as a theoretical justification for choosing this measure of risk.Si un agent économique rationnel est moins sensible au niveau de son revenu qu'à l'utilité de celui-ci, effectuer des tests de dominance stochastique n'a de sens que si ces tests portent sur les utilités de revenus aléatoires. On peut alors montrer que cet agent est caractérisé par une fonction d'utilité élémentaire telle que les utilités des revenus aléatoires ne violent jamais la dominance stochastique de second ordre. Le préordre induit par la dominance stochastique est alors aussi proche que possible du préordre des préférences et l'on peut généraliser la notion de risque à la Rothschild et Stiglitz en raisonnant en terme de risque "subjectif" où les valeurs sont exprimées en utilités. On peut enfin poser un axiome d'indépendance affaibli qui n'est valide que pour les revenus aléatoires "comparables" c'est-à-dire ceux qui ont la même espérance d'utilité. Cette nouvelle axiomatisation du comportement d'un individu en univers incertain aboutit à une théorie de la déception où la fonctionnelle représentant les préférences est "loterie-dépendante" (Becker and Sarin 1987). Si l'utilité marginale de l'investisseur est constante, la nouvelle fonctionnelle n'est que l'opposé d'une mesure de risque convexe (Föllmer and Shied 2002) et elle peut constituer la justification de celle-ci

Stochastic dominance, risk and disappointment: a synthesis

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2016.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2014.54RR - ISSN : 1955-611X - Version originale Juin 2014, révisée Juillet 2015, révisée Janvier 2016In this article, utilities are substituted for monetary values in the definition of second order stochastic dominance (SSD). Doing so yields a family of preorders induced by SSD among which one is the "closest" to the original preorder of preferences. The corresponding utility function is the most likely to be that of the decision maker. It may be defined before behavioural axioms are set. Theories of decision making under risk can then be restated in a more general and consistent way. As an example, a new theory of disappointment is developed, which is endowed with three important properties: (a) risk premia are invariant by translation, (b) when constant marginal utility is assumed, preferences are represented by a functional which is the opposite to a convex measure of risk and (c) the functional representing preferences and the utility function can be easily elicited through experimental testing.Une fonction d'utilité est une bijection des loteries "ordinaires" sur des loteries où des "utilités" auront été substituées aux revenus monétaires. On peut définir une dominance stochastique de second ordre sur ces loteries qui est "subjective" parce qu'elle dépend de la fonction retenue. Parmi les préordres induits par ces dominances stochastiques, il en est un qui est le plus "proche" des préférences de l'agent économique considéré. Il correspond à une fonction d'utilité qui apparaît comme étant la plus vraisemblable pour décrire le comportement de l'agent ; elle peut être déterminée avant que soit mise en place un jeu d'axiomes caractérisant la rationalité des choix en univers risqué. N'importe quelle théorie de la décision peut alors être reformulée compte tenu de ce que cette fonction d'utilité doit être celle de l'agent. A titre d'application, nous reformulons une théorie de la déception où la fonctionnelle représentant les préférences est "loterie-dépendante". Cette théorie possède trois propriétés très intéressantes : (a) les primes de risque sont invariantes par translation (b) la fonctionnelle représentant les préférences n'est autre que l'opposé d'une mesure convexe de risque (Föllmer et Schied 2002), si l'utilité marginale de la richesse est constante et (c) l'on peut déterminer la fonction d'utilité élémentaire à partir de tests empiriques

Disappointment Models: an axiomatic approach

URL des Documents de travail : http://ces.univ-paris1.fr/cesdp/cesdp2011.htmlDocuments de travail du Centre d'Economie de la Sorbonne 2010.102 - ISSN : 1955-611X - Version originale Décembre 2010, révisée en Mai et Décembre 2011In this paper, a fully choice-based theory of disappointment is developed. It encompasses, as particular cases, EU theory, Gul's theory of disappointment (1991) and the models of Loomes and Sugden (1986). According to the new theory, the risk premium of a random prospect is the sum of two premiums: a concavity premium that is nothing but the usual Arrow-Pratt premium and a second premium that may be identified to expected disappointment. The corresponding representing functional belongs to the class of lottery-dependent utility models (Becker and Sarin 1987) since disappointment is the deficit between the utility of the realized outcome and its expected value. However, unlike the lottery-dependent approach, the theory is choice-based and its axioms are experimentally testable.Nous proposons, dans cette étude, une axiomatisation du comportement d'un individu en univers incertain. Cette axiomatisation permet d'effectuer une synthèse de nombreuses théories antérieures : théorie de l'utilité espérée, théorie de la déception (Gul 1991), modèles à la Loomes et Sugden (1986) ou modèles à fonctionnelle "loterie-dépendante" (Becker and Sarin 1987). La prime de risque exigée par un investisseur y est la somme d'une prime d'Arrow-Pratt et d'une seconde prime, égale à l'espérance de la déception. Celle-ci n'est autre que la différence entre la satisfaction éprouvée ex ante et l'utilité espérée du revenu aléatoire

Disappointment Models : an axiomatic approach

In this paper, a fully choice-based theory of disappointment is developed. It encompasses, as particular cases, EU theory, Gul's theory of disappointment (1991) and the models of Loomes and Sugden (1986). According to the new theory, the risk premium of a random prospect is the sum of two premiums : a concavity premium that is nothing but the usual Arrow-Pratt premium and a second premium that may be identified to expected disappointment. The corresponding representing functional belongs to the class of lottery-dependent utility models (Becker and Sarin 1987) since disappointment is the deficit between the utility of the realized outcome and its expected value. However, unlike the lottery-dependent approach, the theory is choice-based and its axioms are experimentally testable.Axiomatization ; disappointment aversion ; random prospect ; risk premium ; expected utility.

Low temperature reflectivity study of ZnO/(Zn,Mg)O quantum wells grown on M-plane ZnO substrates

We report growth of high quality ZnO/Zn0.8Mg0.2O quantum well on M-plane oriented ZnO substrates. The optical properties of these quantum wells are studied by using reflectance spectroscopy. The optical spectra reveal strong in-plane optical anisotropies, as predicted by group theory, and marked reflectance structures, as an evidence of good interface morphologies. Signatures ofc onfined excitons built from the spin-orbit split-off valence band, the analog of exciton C in bulk ZnO are detected in normal incidence reflectivity experiments using a photon polarized along the c axis of the wurtzite lattice. Experiments performed in the context of an orthogonal photon polarization, at 90^{\circ}; of this axis, reveal confined states analogs of A and B bulk excitons. Envelope function calculations which include excitonic interaction nicely account for the experimental report

Volatility Models : from GARCH to Multi-Horizon Cascades

We overview different methods of modeling volatility of stock prices and exchange rates, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of price fluctuations vary across the time scales of observation. The adequacy of different models for describing price dynamics at several time horizons simultaneously is the central topic of this study. We propose a detailed survey of recent volatility models, accounting for multiple horizons. These models are based on different and sometimes competing theoretical concepts. They belong either to GARCH or stochastic volatility model families and often borrow methodological tools from statistical physics. We compare their properties and comment on their pratical usefulness and perspectives.Volatility modeling, GARCH, stochastic volatility, volatility cascade, multiple horizons in volatility.

Transport of indirect excitons in ZnO quantum wells

We report on spatially- and time-resolved emission measurements and observation of transport of indirect excitons in ZnO/MgZnO wide single quantum wells