arXiv subjects

Julien Guyon

Publications and source records attributed to Julien Guyon.

7 recordsLinked to original sources

arXiv2026

A single multi-configuration Direct Electron Detector for various electron imaging and diffraction-based techniques in SEM

Addressing the need for efficient and integrated multiscale crystallographic and defect analyses of advanced materials, this paper presents the implementation of a new multi-configuration detection system, integrating a single Timepix3-based direct electron detector (DED) in a scanning electron microscope (SEM). By combining precise translation and rotation movements, this system enables, for the first time, the use of the same detector to realize all principal diffraction geometries. These include conventional Electron BackScatter Diffraction (EBSD), off-axis Reflexion Kikuchi Diffraction (RKD), and Transmission Kikuchi Diffraction (TKD) in on-, off- and near-axis configurations. Furthermore, transitions between all these geometries are accomplished without hardware modification. On the other hand, this work presents efficient reconstruction of electron images using the detector data-driven feature, extending thus its applicability to BackScattered Electron imaging (BSE), Electron Channelling Contrast Imaging (ECCI) and Scanning Transmission Electron Imaging in SEM (STEM-in-SEM) characterizations. High-quality Kikuchi patterns easily indexable were acquired across all geometries as well as micrographs of dislocations in both reflection and transmission modes. This is achieved thanks to the flexibility of the implemented detector, the optimizations made in acquisition parameters, such as energy filtering settings, and the efficiency of the developed custom approach used for electron data post-processing. Through this work, it is demonstrated that with a single DED assisted by an orientable support, it is possible to perform multiple advanced microstructural characterizations of both bulk samples and thin foils in the same SEM.

physics.ins-det↗

arXiv2025

On the surjectivity of the conditional expectation given a real random variable

In this paper, we investigate the distributions of random couples $(X,Y)$ with $X$ real-valued such that any non-negative integrable random variable $f(X)$ can be represented as a conditional expectation, $f(X)=\mathbb{E}[g(Y)|X]$, for some non-negative measurable function $g$. It turns out that this representation property is related to the smallness of the support of the conditional law of $X$ given $Y$, and in particular fails when this conditional law almost surely has a non-zero absolutely continuous component with respect to the Lebesgue measure. We give a sufficient condition for the representation property and check that it is also necessary under some additional assumptions (for instance when $X$ or $Y$ are discrete). We also exhibit a rather involved example where the representation property holds but the sufficient condition does not. Finally, we discuss a weakened representation property where the non-negativity of $g$ is relaxed. This study is motivated by the calibration of time-discretized path-dependent volatility models to the implied volatility surface.

math.PR↗

arXiv2024

Pricing and calibration in the 4-factor path-dependent volatility model

We consider the path-dependent volatility (PDV) model of Guyon and Lekeufack (2023), where the instantaneous volatility is a linear combination of a weighted sum of past returns and the square root of a weighted sum of past squared returns. We discuss the influence of an additional parameter that unlocks enough volatility on the upside to reproduce the implied volatility smiles of S\&P 500 and VIX options. This PDV model, motivated by empirical studies, comes with computational challenges, especially in relation to VIX options pricing and calibration. We propose an accurate \emph{pathwise} neural network approximation of the VIX which leverages on the Markovianity of the 4-factor version of the model. The VIX is learned pathwise as a function of the Markovian factors and the model parameters. We use this approximation to tackle the joint calibration of S\&P 500 and VIX options, quickly sample VIX paths, and price derivatives that jointly depend on S\&P 500 and VIX. As an interesting aside, we also show that this \emph{time-homogeneous}, low-parametric, Markovian PDV model is able to fit the whole surface of S\&P 500 implied volatilities remarkably well.

q-fin.CP↗

arXiv2019

Inversion of Convex Ordering: Local Volatility Does Not Maximize the Price of VIX Futures

It has often been stated that, within the class of continuous stochastic volatility models calibrated to vanillas, the price of a VIX future is maximized by the Dupire local volatility model. In this article we prove that this statement is incorrect: we build a continuous stochastic volatility model in which a VIX future is strictly more expensive than in its associated local volatility model. More generally, in this model, strictly convex payoffs on a squared VIX are strictly cheaper than in the associated local volatility model. This corresponds to an inversion of convex ordering between local and stochastic variances, when moving from instantaneous variances to squared VIX, as convex payoffs on instantaneous variances are always cheaper in the local volatility model. We thus prove that this inversion of convex ordering, which is observed in the SPX market for short VIX maturities, can be produced by a continuous stochastic volatility model. We also prove that the model can be extended so that, as suggested by market data, the convex ordering is preserved for long maturities.

q-fin.MF↗

arXiv2017

Bounds for VIX Futures given S&P 500 Smiles

We derive sharp bounds for the prices of VIX futures using the full information of S&P 500 smiles. To that end, we formulate the model-free sub/superreplication of the VIX by trading in the S&P 500 and its vanilla options as well as the forward-starting log-contracts. A dual problem of minimizing/maximizing certain risk-neutral expectations is introduced and shown to yield the same value. The classical bounds for VIX futures given the smiles only use a calendar spread of log-contracts on the S&P 500. We analyze for which smiles the classical bounds are sharp and how they can be improved when they are not. In particular, we introduce a family of functionally generated portfolios which often improves the classical bounds while still being tractable; more precisely, determined by a single concave/convex function on the line. Numerical experiments on market data and SABR smiles show that the classical lower bound can be improved dramatically, whereas the upper bound is often close to optimal.

q-fin.PR↗

arXiv2007

Limit theorems for bifurcating Markov chains. Application to the detection of cellular aging

We propose a general method to study dependent data in a binary tree, where an individual in one generation gives rise to two different offspring, one of type 0 and one of type 1, in the next generation. For any specific characteristic of these individuals, we assume that the characteristic is stochastic and depends on its ancestors' only through the mother's characteristic. The dependency structure may be described by a transition probability $P(x,dy dz)$ which gives the probability that the pair of daughters' characteristics is around $(y,z)$, given that the mother's characteristic is $x$. Note that $y$, the characteristic of the daughter of type 0, and $z$, that of the daughter of type 1, may be conditionally dependent given $x$, and their respective conditional distributions may differ. We then speak of bifurcating Markov chains. We derive laws of large numbers and central limit theorems for such stochastic processes. We then apply these results to detect cellular aging in Escherichia Coli, using the data of Stewart et al. and a bifurcating autoregressive model.

math.PR↗

arXiv2007

Euler Scheme and Tempered Distributuions

Given a smooth R^d-valued diffusion, we study how fast the Euler scheme with time step 1/n converges in law. To be precise, we look for which class of test functions f the approximate expectation E[f(X^{n,x}_1)] converges with speed 1/n to E[f(X^x_1)]. If X is uniformly elliptic, we show that this class contains all tempered distributions, and all measurable functions with exponential growth. We give applications to option pricing and hedging, proving numerical convergence rates for prices, deltas and gammas.

math.PR↗