American Options Based on Malliavin Calculus and Nonparametric Variance Reduction Methods

This paper is devoted to pricing American options using Monte Carlo and the Malliavin calculus. Unlike the majority of articles related to this topic, in this work we will not use localization fonctions to reduce the variance. Our method is based on expressing the conditional expectation E[f(St)/Ss] using the Malliavin calculus without localization. Then the variance of the estimator of E[f(St)/Ss] is reduced using closed formulas, techniques based on a conditioning and a judicious choice of the number of simulated paths. Finally, we perform the stopping times version of the dynamic programming algorithm to decrease the bias. On the one hand, we will develop the Malliavin calculus tools for exponential multi-dimensional diffusions that have deterministic and no constant coefficients. On the other hand, we will detail various nonparametric technics to reduce the variance. Moreover, we will test the numerical efficiency of our method on a heterogeneous CPU/GPU multi-core machine

De l'inflexion des normes temporelles à la redéfinition de 'l'éthos professionnel'. L'exemple des femmes dans les professions libérales en France

Ce texte vise à rendre compte de l'expérience des femmes exerçant leur activité dans trois groupes professionnels : les médecins, les avocat∙e*s et les architectes. Il s'attache particulièrement à saisir, à partir de l'analyse des pratiques professionnelles et familiales, les modes de transformation de " l'éthos professionnel " prévalent au sein des professions libérales en France. Cette reconfiguration des manières d'exercer sa profession au quotidien passe essentiellement par une redéfinition des rapports que les individus entretiennent aux différents temps sociaux. Ainsi, cette activité entraîne un intense travail de " torsion " des normes temporelles auquel se livrent les professionnelles

Post-harvest disease : Effects of the physiological age of bananas on their susceptibility to wound anthracnose caused by Colletotrichum musae

Wound anthracnose caused by Colletotrichum e, and early ripening are the main problems affecting the quality of export bananas from a lot of countries in the world. In the case of Guadeloupe in French West Indies, these problems generally concern bananas grown in lowland plantations during the rainy season. Three experiments were carried out to study the influence of the physiological age of bananas (calculated on the basis of mean daily temperature sums) on their susceptibility to anthracnose. Stressful growing conditions, especially soil flooding, slowed fruit growth but had no direct effect on fruit susceptibility to C. e or on the green life. However, fruit that had accumulated lower temperature sums were less susceptible to wound anthracnose. By varying the source-sink ratio, we show that bananas of the same grade but different physiological ages had markedly different susceptibility to C. e. Bananas with the same temperature sum accumulation but grown in different soil-climate conditions had different levels of susceptibility. Fruit grown in cooler, highland areas were less susceptible to C. e than fruit of the same physiological age from lowland plantations. Our results suggest that temperature sum accumulation rate is a critical factor affecting the susceptibility of bananas to the pathogen. (Texte intégral

Banana susceptibility to wound anthracnose : Effects of flooding, early-harvesting, and source-sink ratio modification

WOUND anthracnose, caused by the fungus Colletotrichum musae, has a major impact on the quality of export bananas worldwide. Fruits harvested at an advanced physiological age seem to be more susceptible to anthracnose. We examined the relationship between the fruit physiological age, measured by the temperature sum (in degree days - dd), and the susceptibility to wound anthracnose by analysing the effects of three factors: - Flooding - a stressful growing condition - in a greenhouse; - Early harvesting of bananas under two climatic conditions; - Source-sink ratio modification by removal of leaves or hands. (Texte intégral

Convenient Multiple Directions of Stratification

This paper investigates the use of multiple directions of stratification as a variance reduction technique for Monte Carlo simulations of path-dependent options driven by Gaussian vectors. The precision of the method depends on the choice of the directions of stratification and the allocation rule within each strata. Several choices have been proposed but, even if they provide variance reduction, their implementation is computationally intensive and not applicable to realistic payoffs, in particular not to Asian options with barrier. Moreover, all these previously published methods employ orthogonal directions for multiple stratification. In this work we investigate the use of algorithms producing convenient directions, generally non-orthogonal, combining a lower computational cost with a comparable variance reduction. In addition, we study the accuracy of optimal allocation in terms of variance reduction compared to the Latin Hypercube Sampling. We consider the directions obtained by the Linear Transformation and the Principal Component Analysis. We introduce a new procedure based on the Linear Approximation of the explained variance of the payoff using the law of total variance. In addition, we exhibit a novel algorithm that permits to correctly generate normal vectors stratified along non-orthogonal directions. Finally, we illustrate the efficiency of these algorithms in the computation of the price of different path-dependent options with and without barriers in the Black-Scholes and in the Cox-Ingersoll-Ross markets.Comment: 21 pages, 11 table

Multi-step Richardson-Romberg Extrapolation: Remarks on Variance Control and complexity

We propose a multi-step Richardson-Romberg extrapolation method for the computation of expectations $E f(X_{_T})$ of a diffusion $(X_t)_{t\in [0,T]}$ when the weak time discretization error induced by the Euler scheme admits an expansion at an order $R\ge 2$. The complexity of the estimator grows as $R^2$ (instead of $2^R$) and its variance is asymptotically controlled by considering some consistent Brownian increments in the underlying Euler schemes. Some Monte carlo simulations carried with path-dependent options (lookback, barriers) which support the conjecture that their weak time discretization error also admits an expansion (in a different scale). Then an appropriate Richardson-Romberg extrapolation seems to outperform the Euler scheme with Brownian bridge.Comment: 28 pages, \`a para\^itre dans Monte Carlo Methods and Applications Journa