Dans la théorie des processus stochastiques, une martingale locale est un processus stochastique qui est localement une martingale, ce qui signifie qu'il y a une suite de localisation de temps d'arrêt et que le processus arrêté est une martingale. Definition Soi (\Omega,\mathcal{F},\mathbb{F},P) un espace de probabilité filtré et un processus \mathbb{F}-adapté X=(X_t)_{t\geq 0} avec X_0=0 (zéro à zéro). S'il existe une suite non décroissante (T_n)_{n\in\mathbb{N}} de temps d'arrêt de \mathbb{F} telle que

P\left(\lim\limits_{n\to \infty}T_n=\infty\right)=1 et

pour tout n\in \mathbb{N } le processus arrêté X^{(n)}=(X_t^{(n)})_{t\geq 0} défini par X^{(n)}t\overset{\Delta}{=} X{t\wedge T_n} soit une martingale,

alors on appelle X une martingale locale et on écrit X\in \mathcal{M}^{\operatorname{loc}}. Si X

Essays in Empirical Asset Pricing

Alexis Arilès Marchal

This thesis consists of three applications of machine learning techniques to empirical asset pricing.In the first part, which is co-authored work with Oksana Bashchenko, we develop a new method that detects jumps nonparametrically in financial time series and significantly outperforms the current benchmark on simulated data. We use a long short-term memory (LSTM) neural network that is trained on labelled data generated by a process that experiences both jumps and volatility bursts. As a result, the network learns how to disentangle the two. Then it is applied to out-of-sample simulated data and delivers results that considerably differ from the benchmark: we obtain fewer spurious detection and identify a larger number of true jumps. When applied to real data, our approach for jump screening allows to extract a more precise signal about future volatility.In the second part, which is co-authored work with Oksana Bashchenko, we develop a methodology for detecting asset bubbles using a neural network. We rely on the theory of local martingales in continuous-time and use a deep network to estimate the diffusion coefficient of the price process more accurately than the current estimator, obtaining an improved detection of bubbles. We show the outperformance of our algorithm over the existing statistical method in a laboratory created with simulated data. We then apply the network classification to real data and build a zero net exposure trading strategy that exploits the risky arbitrage emanating from the presence of bubbles in the US equity market from 2006 to 2008. The profitability of the strategy provides an estimation of the economical magnitude of bubbles as well as support for the theoretical assumptions relied on.In the third part, I propose a new tool to characterize the resolution of uncertainty around FOMC press conferences. It relies on the construction of a measure capturing the level of discussion complexity between the Fed Chair and reporters during the Q&A sessions. I show that complex discussions are associated with higher equity returns and a drop in realized volatility. The method creates an attention score by quantifying how much the Chair needs to rely on reading internal documents to be able to answer a question. This is accomplished by building a novel dataset of video images of the press conferences and leveraging recent deep learning algorithms from computer vision. This alternative data provides new information on nonverbal communication that cannot be extracted from the widely analyzed FOMC transcripts. This chapter can be seen as a proof of concept that certain videos contain valuable information for the study of financial markets.

EPFL2022

Informational Efficiency under Short Sale Constraints

Martin Larsson

A constrained informationally efficient market is defined as one in which the price process arises as the outcome of some equilibrium where agents face restrictions on trade. This paper investigates the case of short sale constraints, a setting which, despite its simplicity, generates new insights. In particular, it is shown that short sale constrained informationally efficient markets always admit equivalent supermartingale measures and local martingale deflators, but not necessarily local martingale measures. In addition, if some local martingale deflator turns the price process into a true martingale, then the market is constrained informationally efficient. Examples are given to illustrate the subtle phenomena that can arise in the presence of short sale constraints, with particular attention given to representative agent equilibria and the different notions of no arbitrage.

Siam Publications2015

Essays in Empirical Asset Pricing

Alexis Arilès Marchal

EPFL2022

Martingale locale

P\left(\lim\limits_{n\to \infty}T_n=\infty\right)=1 et

pour tout n\in \mathbb{N } le processus arrêté X^{(n)}=(X_t^{(n)})_{t\geq 0} défini par X^{(n)}t\overset{\Delta}{=} X{t\wedge T_n} soit une martingale,

Essays in Empirical Asset Pricing

Informational Efficiency under Short Sale Constraints

Informational Efficiency under Short Sale Constraints

Essays in Empirical Asset Pricing