Auswahl der wissenschaftlichen Literatur zum Thema „Choquet pricing“

It is known that the quasi-arithmetic means can be characterized in various ways, with an essential role of a symmetry property. In the expected utility theory, the quasi-arithmetic mean is called the certainty equivalent and it is applied, e.g., in a utility-based insurance contracts pricing. In this paper, we introduce and study the quasi-arithmetic type mean in a more general setting, namely with the expected value being replaced by the generalized Choquet integral. We show that a functional that is defined in this way is a mean. Furthermore, we characterize the equality, positive homogeneity, and translativity in this class of means.

AbstractWhen prices of assets traded in a financial market are determined by nonlinear pricing rules, different parities between call and put options have been considered. We show that, under monotonicity, parities between call and put options and discount certificates characterize ambiguity‐sensitive (Choquet and/or Šipoš) pricing rules, that is, pricing rules that can be represented via discounted expectations with respect to non‐additive probability measures. We analyze how nonadditivity relates to arbitrage opportunities and we give necessary and sufficient conditions for Choquet and Šipoš pricing rules to be arbitrage free. Finally, we identify violations of the Call‐Put Parity with the presence of bid–ask spreads.

AbstractThe fundamental theory of asset pricing has been developed under the two main assumptions that markets are frictionless and have no arbitrage opportunities. In this case the market enforces that replicable assets are valued by a linear function of their payoffs, or as the discounted expectation with respect to the so-called risk-neutral probability. Important evidence of the presence of frictions in financial markets has led to study market pricing rules in such a framework. Recently, Cerreia-Vioglio et al. (J Econ Theory 157:730–762, 2015) have extended the Fundamental Theorem of Finance by showing that, with markets frictions, requiring the put–call parity to hold, together with the mild assumption of translation invariance, is equivalent to the market pricing rule being represented as a discounted Choquet expectation with respect to a risk-neutral nonadditive probability. This paper continues this study by characterizing important properties of the (unique) risk-neutral nonadditive probability $$v_f$$ v f associated with a Choquet pricing rule f, when it is not assumed to be subadditive. First, we show that the observed violation of the call–put parity, a condition considered by Chateauneuf et al. (Math Financ 6:323–330, 1996) similar to the put–call parity in Cerreia-Vioglio et al. (2015), is consistent with the existence of bid-ask spreads. Second, the balancedness of $$v_f$$ v f —or equivalently the non-vacuity of its core—is characterized by an arbitrage-free condition that eliminates all the arbitrage opportunities that can be obtained by splitting payoffs in parts; moreover the (nonempty) core of $$v_f$$ v f consists of additive probabilities below $$v_f$$ v f whose associated (standard) expectations are all below the Choquet pricing rule f. Third, by strengthening again the previous arbitrage-free condition, we show the existence of a strictly positive risk-neutral probability below $$v_f$$ v f , which allows to recover the standard formulation of the Fundamental Theorem of Finance for frictionless markets.

Cette thèse vise à fournir des méthodes théoriques et empiriques innovantes dans le cadre de l'évaluation des actifs financiers aux chercheurs en économie, aux teneurs de marché et aux différents acteurs de marché, dont les courtiers, les négociants, les gestionnaires d'actifs et les régulateurs. Nous proposons une extension du théorème fondamental de l'évaluation des actifs (FTAP) adaptée aux marchés présentant des frictions financières. Par conséquent, nos méthodes d'évaluation des actifs permettent d'obtenir un système de prix présentant des bid-ask spreads (écarts entre le prix d’achat et de vente), tels qu'ils sont observés sur les marchés financiers ce qui les rendent plus facilement interprétables. Dans le premier chapitre, nous introduisons deux théorèmes de représentation pour l'évaluation des actifs financiers sur les marchés à deux dates, en tenant compte d'une variété de frictions financières (coûts de transaction, taxes, frais de commission). Ce résultat repose sur une nouvelle condition d'absence d'arbitrage adaptée au marché avec frictions financières, qui prend en compte les stratégies potentielles d'achat et de vente. En outre, ces modèles d'évaluation des actifs reposent tous deux sur des mesures de probabilité non additives. Le premier modèle est une règle de prix de Choquet, pour laquelle nous proposons un cas particulier adapté à la calibration, et le second est une règle d'évaluation à priors multiples. Dans le deuxième chapitre, en vue de généraliser nos modèles d'évaluation des actifs, nous fournissons les conditions nécessaires et suffisantes pour des règles de prix de Choquet en multi-périodes caractérisées notamment par l’existence des bid-ask spreads. Nous montrons qu'il est possible de modéliser un problème de tarification dynamique sur plusieurs périodes par un problème de tarification sur une période lorsque la filtration est sans friction, ce qui est équivalent à supposer la propriété de martingale, qui est équivalente à supposer la cohérence des prix. Enfin, dans le troisième chapitre, nous présentons l'axiomatisation d'une classe particulière de règles de prix de Choquet, à savoir les règles de tarification dépendantes du rang qui supposent aussi l'absence d'arbitrage et la parité put-call (entre les options de vente et les options d'achat). Les règles de prix dépendantes du rang ont l'avantage d'être facilement calibrées car la mesure de probabilité non additive prend la forme de la probabilité objective distordue. Nous proposons donc une étude empirique de ces règles de prix dépendantes du rang par le biais d'une calibration paramétrique sur des données de marché afin d'explorer l'impact des frictions financières sur les prix. Nous étudions également la validité empirique de la parité put-call. En outre, nous étudions l'impact du délai d'expiration (valeur temps) et de la moneyness (valeur intrinsèque) sur la forme de la fonction de distorsion. Nous trouvons que les règles de prix dépendantes du rang qui en résultent sont toujours plus précises que la règle de référence (FTAP). Enfin, nous établissons un lien entre les frictions du marché et l'aversion au risque du marché
This thesis aims to provide innovative theoretical and empirical methods for valuing securities to economics researchers, market makers, and participants, including brokers, dealers, asset managers, and regulators. We propose an extension of the Fundamental Theorem of Asset Pricing (FTAP) tailored to markets with financial frictions. Hence, our asset pricing methodologies allow for more tractable bid and ask prices, as observed in the financial market. This thesis provides both theoretical models and an empirical application of the pricing rule with bid-ask spreads.In our first chapter, we introduce two straightforward closed-form pricing expressions for securities in two-date markets, encompassing a variety of frictions (transaction cost, taxes, commission fees). This result relies on a novel absence of arbitrage condition tailored to the market with frictions considering potential buy and sell strategies. Furthermore, these asset pricing models both rely on non-additive probability measures. The first is a Choquet pricing rule, for which we offer a particular case adapted for calibration, and the second is a Multiple Priors pricing rule.In the second chapter, as a step toward generalizing our asset pricing models, we provide the necessary and sufficient conditions for multi-period pricing rules characterized by bid-ask spreads. We extend the multi-period version of the Fundamental Theorem of Asset Pricing by assuming the existence of market frictions. We show that it is possible to model a dynamic multi-period pricing problem with a one-stage pricing problem when the filtration is frictionless, which is equivalent to assuming the martingale property, which is equivalent to assuming price consistency.Finally, in the third chapter, we give the axiomatization of a particular class of Choquet pricing rule, namely Rank-Dependent pricing rules assuming the absence of arbitrage and put-call parity. Rank-dependent pricing rules have the appealing feature of being easily calibrated because the non-additive probability measure takes the form of a distorted objective probability. Therefore, we offer an empirical study of these Rank-Dependent pricing rules through a parametric calibration on market data to explore the impact of market frictions on prices. We also study the empirical validity of the put-call parity. Furthermore, we investigate the impact of time to expiration (time value) and moneyness (intrinsic value) on the shape of the distortion function. The resulting rank-dependent pricing rules always exhibit a greater accuracy than the benchmark (FTAP). Finally, we relate the market frictions to the market's risk aversion