A multi-layer, multi-node ReLU network is a powerful, efficient, and popular tool in statistical prediction tasks. However, in contrast to the great emphasis on its empirical applications, its statistical properties are rarely investigated which is mainly due to its severe nonlinearity and heavy...

Carr and Wu (2004), henceforth CW, developed a framework that encompasses almost all of the continuous-time models proposed in the option pricing literature. Their framework hinges on the stopping time property of the time changes. By ana- lyzing the measurability of the time changes with...

This paper investigates the performance of different parametric models, stable and tempered stable distributions, for capturing the tail behaviour of the log-returns. We first define and discuss the properties of the stable and tempered stable random variables. We then show how to estimate their...

If the closed-form formula for the probability density function is not available, implementing the maximum likelihood estimation is challenging. We introduce a simple, fast, and accurate way for the estimation of numerous distributions that belong to the class of tempered stable probability...

To facilitate crossing from the "black box" to "glass box" in the application of neural networks (NNs), we develop a variable significant test for the multi-layer perceptrons. To derive the test statistic and its asymptotic distribution, we provide the consistency of the multi-layer perceptrons...

To facilitate crossing from the "black box" to "glass box" in the application of neural net- works, we extend Horel and Giesecke (2020) and develop a variable/feature significant test for multi-layer perceptrons (MLP). The proposed test permits one to assess the statistical significance of the...

We empirically study sources of abnormal changes, henceforth jumps, simultaneously in investor beliefs and asset prices using 164 million tweets from a social media investing platform, StockTwits. Before the COVID-19 pandemic, we find that on average 4.88% (7.88%) jumps in asset prices (investor...

Social interaction and information transmission are essential components of pricing and trading in financial markets. To investigate the behavior contagion and information cascades among investors and sectors, we deploy a jump-diffusion process on investor sentiment -- a novel dataset from...

We empirically explore the role of investor disagreement and news for various types of stock jumps, where the dynamic of stock returns is captured by a contagion model. Our disagreement measure is derived from more than 173 million tweets from a social media investing platform, StockTwits, for...