Stationary Heston model: Calibration and Pricing of exotics using Product Recursive Quantization

A major drawback of the Standard Heston model is that its implied volatility surface does not produce a steep enough smile when looking at short maturities. For that reason, we introduce the Stationary Heston model where we replace the deterministic initial condition of the volatility by its invariant measure and show, based on calibrated parameters, that this model produce a steeper smile for short maturities than the Standard Heston model. We also present numerical solution based on Product Recursive Quantization for the evaluation of exotic options (Bermudan and Barrier options)

Quantization-based Bermudan option pricing in the FX world

This paper proposes two numerical solution based on Product Optimal Quan-tization for the pricing of Foreign Echange (FX) linked long term Bermudan options e.g. Bermudan Power Reverse Dual Currency options, where we take into account stochastic domestic and foreign interest rates on top of stochastic FX rate, hence we consider a 3-factor model. For these two numerical methods, we give an estimation of the $L^2$-error induced by such approximations and we illustrate them with market-based examples that highlight the speed of such methods

Reactions to psychological contract breaches and organizational citizenship behaviours: An experimental manipulation of severity

Copyright © 2018 John Wiley & Sons, Ltd. Grounded in affective events theory, we investigated the effects of experimentally manipulated psychological contract breaches on participants\u27 feelings of violation, subsequent perceptions of psychological contract strength, and organizational citizenship behaviours in a sample of working adults. Results support previous findings that pre-existing relational psychological contract strength interacts with severity of unmet promises or expectations. Specifically, individuals with high relational contracts who experience low severity of unmet promises/expectations have the lowest breach perceptions, whereas individuals with high relational contracts who experience more severe levels unmet promises/expectations experience the highest level of breach perceptions. Results also support the concept of a breach spiral in that prior perceptions of breach led to an increased likelihood of subsequent perceptions of breach following the experimental manipulation. Furthermore, consistent with affective events theory, results support the argument that a psychological contract breach\u27s effect on specific organizational citizenship behaviours is mediated by feelings of violation and the reassessment of relational contracts. These effects were present even after controlling for the direct effects of the manipulated severity of unmet promises/expectations

Méthodes numériques par quantification optimale en finance

This thesis is divided into four parts that can be read independently. In this manuscript, we make some contributions to the theoretical study and financial applications of optimal quantization. In the first part, we recall the theoretical foundations of optimal quantization as well as the classical numerical methods to build optimal quantizers. The second part focuses on the problem of numerical integration in dimension 1. This problem arises when one wishes to numerically compute expectations, such as the valuation of derivatives in finance that are expressed as the expectation of a function of a single financial asset. We recall the existing strong and weak error results and extend the results of order 2 convergence rate to other function classes with less regularity. In a second step, we present a weak error development result in one dimension and a second development in a higher dimension when the chosen quantizer is a product quantizer. In the third part, we look at a first numerical application. We introduce a stationary Heston model in which the initial condition of volatility, instead of being deterministic as in the standard model, is assumed to be randomly distributed with the stationary distribution of the CIR EDS governing volatility. This variant of the original Heston model produces for European options on short maturities a steeper smile of implied volatility than the standard model. We then develop a product recursive quantization-based numerical method for the valuation of Bermudan options and barriers. The fourth and last part deals with a second numerical application, the pricing of Bermudan exchange rate options in a 3 factor model, i.e. where the exchange rate, domestic and foreign interest rates are stochastic. These products are known in the markets as PRDC (Power Reverse Dual Currency). We propose two schemes to evaluate this type of options, both based on optimal product quantization and establish a priori error estimates.Cette thèse est divisée en quatre parties pouvant être lues indépendamment. Dans ce manuscrit, nous apportons quelques contributions à l’étude théorique et aux applications en finance de la quantification optimale. Dans la première partie, nous rappelons les fondements théoriques de la quantification optimale ainsi que les méthodes numériques classiques pour construire des quantifieurs optimaux. La seconde partie se concentre sur le problème d’intégration numérique en dimension 1. Ce problème apparait lorsque l’on souhaite calculer numériquement des espérances, tel que l’évaluation de produits dérivés. Nous y rappelons les résultats d’erreurs forts et faibles existants et étendons les résultats des convergences d’ordre 2 à d’autres classes de fonctions moins réguliers. Dans un deuxième temps, nous présentons un résultat de développement d’erreur faible en dimension 1 et un second développement en dimension supérieure pour un quantifieur produit. Dans la troisième partie, nous nous intéressons à une première application numérique. Nous introduisons un modèle de Heston stationnaire dans lequel la condition initiale de la volatilité est supposée aléatoire de loi la distribution stationnaire de l’EDS du CIR régissant la volatilité. Cette variante du modèle de Heston original produit pour les options européennes sur les maturités courtes un smile de volatilité implicite plus prononcé que le modèle standard. Nous développons ensuite une méthode numérique à base de quantification récursive produit pour l’évaluation d’options bermudiennes et barrières. La quatrième et dernière partie traite d’une deuxième application numérique, l’évaluation d’options bermudiennes sur taux de change dans un modèle 3 facteurs. Ces produits sont connus sur les marchés sous le noms de PRDC. Nous proposons deux schémas pour évaluer ce type d’options toutes deux basées sur de la quantification optimale produit et établissons des estimations d’erreur à priori

New Weak Error bounds and expansions for Optimal Quantization

International audienceWe propose new weak error bounds and expansion in dimension one for optimal quantization-based cubature formula for different classes of functions, such that piecewise affine functions, Lipschitz convex functions or differentiable function with piecewise-defined locally Lipschitz or α-Hölder derivatives. This new results rest on the local behaviors of optimal quantizers, the L r-L s distribution mismatch problem and Zador's Theorem. This new expansion supports the definition of a Richardson-Romberg extrapolation yielding a better rate of convergence for the cubature formula. An extension of this expansion is then proposed in higher dimension for the first time. We then propose a novel variance reduction method for Monte Carlo estimators, based on one dimensional optimal quantizers