Olivier Torrès

Bio: Olivier Torrès is an academic researcher from Lille University of Science and Technology. The author has contributed to research in topics: Nonparametric statistics & Futures contract. The author has an hindex of 4, co-authored 5 publications receiving 191 citations.

Markovian Processes, Two-Sided Autoregressions and Finite-Sample Inference for Stationary and Nonstationary Autoregressive Processes

Abstract: In this paper, we develop finite-sample inference procedures for stationary and nonstationary autoregressive (AR) models. The method is based on special properties of Markov processes and a split-sample technique. The results on Markovian processes (intercalary independence and truncation) only require the existence of conditional densities. They are proved for possibly nonstationary and/or non-Gaussian multivariate Markov processes. In the context of a linear regression model with AR(1) errors, we show how these results can be used to simplify the distributional properties of the model by conditioning a subset of the data on the remaining observations. This transformation leads to a new model which has the form of a two-sided autoregression to which standard classical linear regression inference techniques can be applied. We show how to derive tests and confidence sets for the mean and/or autoregressive parameters of the model. We also develop a test on the order of an autoregression. We show that a combination of subsample-based inferences can improve the performance of the procedure. An application to U.S. domestic investment data illustrates the method. Dans cet article, nous proposons des procedures d'inference valides a distance finie pour des modeles autoregressifs (AR) stationnaires et non-stationnaires. La methode suggeree est fondee sur des proprietes particulieres des processus markoviens combinees a une technique de subdivision d'echantillon. Les resultats sur les processus de Markov (independance intercalaire, troncature) ne requierent que l'existence de densites conditionnelles. Nous demontrons les proprietes requises pour des processus markoviens multivaries possiblement non-stationnaires et non-gaussiens. Pour le cas des modeles de regression lineaires avec erreurs autoregressives d'ordre un, nous montrons comment utiliser ces resultats afin de simplifier les proprietes distributionnelles du modele en considerant la distribution conditionnelle d'une partie des observations etant donne le reste. Cette transformation conduit a un nouveau modele qui a la forme d'une autoregression bilaterale a laquelle on peut appliquer les techniques usuelles d'analyse des modeles de regression lineaires. Nous montrons comment obtenir des tests et regions de confiance pour la moyenne et les parametres autoregressifs du modele. Nous proposons aussi un test pour l'ordre d'une autoregression. Nous montrons qu'une technique de combinaison de tests obtenus a partir de plusieurs sous-echantillons peut ameliorer la performance de la procedure. Enfin la methode est appliquee a un modele de l'investissement aux Etats-Unis.

Nonparametric Estimation of American Options Exercise Boundaries and Call Prices

Abstract: Unlike European-type derivative securities, there are no simple analytic valuation formulas for American options, even when the underlying asset price has constant volatility. The early exercise feature considerably complicates the valuation of American contracts. The strategy taken in this paper is to rely on nonparametric statistical methods using market data to estimate the call prices and the exercise boundaries. The paper focuses on the daily market option prices and exercise data on the S&P100 contract. A comparison is made with parametric constant volatility model-based prices and exercise boundaries. We find large discrepancies between the parametric and nonparametric call prices and exercise boundaries. Contrairement a ce qu'il est possible d'obtenir dans un contexte d'evaluation de titres derives de type europeen, il n'existe pas de formule analytique simple pour evaluer les options americaines, meme si la volatilite de l'actif sous-jacent est supposee constante. La possibilite d'exercice premature qu'offre ce type de contrat complique considerablement son evaluation. La demarche adoptee dans cette etude consiste a deriver les prix d'option et les frontieres d'exercice a partir de donnees financieres, utilisees dans un cadre d'analyse statistique non-parametrique. Plus particulierement, l'etude utilise les observations quotidiennes du prix du contrat sur l'indice S&P100 ainsi que les observations sur l'exercice de ce contrat. Les resultats sont compares a ceux obtenus a l'aide de techniques parametriques dans un modele ou la volatilite est supposee constante. La conclusion est qu'il existe des differences strategiques entre les predictions des deux modeles, aussi bien en ce qui concerne le prix de l'option que la politique d'exercice qui lui est associee.

Valuing American Options by Simulation: A Simple Least-Squares Approach

Abstract: This article presents a simple yet powerful new approach for approximating the value of American options by simulation. The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniques cannot be used. We illustrate this technique with several realistic examples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an American swaption in a 20-factor string model of the term structure.

Valuing American Options by Simulation: A Simple Least-Squares Approach - eScholarship

Abstract: This article presents a simple yet powerful new approach for approximating the value of American options by simulation. The key to this approach is the use of least squares to estimate the conditional expected payoff to the optionholder from continuation. This makes this approach readily applicable in path-dependent and multifactor situations where traditional finite difference techniqes cannot be used. We illustrate this technique with several realistic examples including valuing an option when the underlying asset follows a jump-diffusion process and valuing an American swaption in a 20-factor string model of the term structure.

Non-Parametric Risk Management and Implied Risk Aversion

Abstract: Typical value-at-risk (VaR) calculations involve the probabilities of extreme dollar losses, based on the statistical distributions of market prices. Such quantities do not account for the fact that the same dollar loss can have two very different economic valuations, depending on business conditions. We propose a nonparametric VaR measure that incorporates economic valuation according to the state-price density associated with the underlying price processes. The state-price density yields VaR values that are adjusted for risk aversion, time preferences, and other variations in economic valuation. In the context of a representative agent equilibrium model, we construct an estimator of the risk-aversion coefficient that is implied by the joint observations on the cross-section of option prices and time-series of underlying asset values.