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...

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...

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...

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...

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 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...

Extensions of expected utility theory are sensitive to the tail behavior of the portfolio return distribution and may not be approximated reliably through higher-order moment expansions. We develop a novel approach for model risk assessment based on a projection method and apply it to portfolio...

We develop a novel class of time-changed Lévy models which are tractable and readily applicable, capture the leverage effect, and exhibit pure jump processes with finite or infinite activity. Our models feature four nested processes reflecting market, volatility and jump risks, and observation...

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...