A hybrid tree/finite-difference approach for Heston-Hull-White type models

We study a hybrid tree-finite difference method which permits to obtain efficient and accurate European and American option prices in the Heston Hull-White and Heston Hull-White2d models. Moreover, as a by-product, we provide a new simulation scheme to be used for Monte Carlo evaluations. Numerical results show the reliability and the efficiency of the proposed method

Rat sensitivity to multipoint statistics is predicted by efficient coding of natural scenes

Efficient processing of sensory data requires adapting the neuronal encoding strategy to the statistics of natural stimuli. Previously, in Hermundstad et al., 2014, we showed that local multipoint correlation patterns that are most variable in natural images are also the most percep-tually salient for human observers, in a way that is compatible with the efficient coding principle. Understanding the neuronal mechanisms underlying such adaptation to image statistics will require performing invasive experiments that are impossible in humans. Therefore, it is important to under-stand whether a similar phenomenon can be detected in animal species that allow for powerful experimental manipulations, such as rodents. Here we selected four image statistics (from single-to four-point correlations) and trained four groups of rats to discriminate between white noise patterns and binary textures containing variable intensity levels of one of such statistics. We interpreted the resulting psychometric data with an ideal observer model, finding a sharp decrease in sensitivity from two-to four-point correlations and a further decrease from four-to three-point. This ranking fully reproduces the trend we previously observed in humans, thus extending a direct demonstration of efficient coding to a species where neuronal and developmental processes can be interrogated and causally manipulated

On Sharp Large Deviations for the bridge of a general Diffusion

We provide sharp Large Deviation estimates for the probability of exit from a domain for the bridge of a $d$-dimensional general diffusion process $X$, as the conditioning time tends to $0$. This kind of results is motivated by applications to numerical simulation. In particular we investigate the influence of the drift $b$ of $X$. It turns out that the sharp asymptotics for the exit time probability are independent of the drift, provided $b$ enjoyes a simple condition that is always satisfied in dimension $1$. On the other hand, we show that the drift can be influential if this assumption is not satisfied.

Using moment approximations to study the density of jump driven SDEs

In order to study the regularity of the density of a solution of a infinite activity jump driven stochastic differential equation we consider the following two-step approximation method. First, we use the solution of the moment problem in order to approximate the small jumps by another whose Lévy measure has finite support. In a second step we replace the approximation of the first two moments by a small noise Brownian motion based on the Assmussen-Rosinski approach. This approximation needs to satisfy certain properties in order to apply the "balance" method which allows the study of densities for the solution process based on Malliavin Calculus for the Brownian motion. Our results apply to situations where the Lévy measure is absolutely continuous with respect to the Lebesgue measure or purely atomic measures or combinations of them

Monte Carlo methods for pricing and hedging American options in high dimension

We numerically compare some recent Monte Carlo algorithms devoted to the pricing and hedging American options in high dimension. In particular, the comparison concerns the quantization method of Barraquand–Martineau and an algorithm based on Malliavin calculus. The (pure) Malliavin calculus algorithm improves the precision of the computation of the delta but, merely for pricing purposes, is uncompetitive with respect to other Monte Carlo methods in terms of computing time. Here, we propose to suitably combine the Malliavin calculus approach with the Barraquand–Martineau algorithm, using a variance reduction technique based on control variables. Numerical tests for pricing and hedging American options in high dimension are given in order to compare the different methodologies

Madrid in progress : developing social housing : a special exhibition for Torino

[101118.EG SBN: "... and the 23. World congress of architects : Torino, 30 june-28 july 2008, Museo regionale di scienze naturali".