We derive a closed-form asymptotic expansion formula for option implied volatility under a two-factor jump-diffusion stochastic volatility model when time-to-maturity is small. Based on numerical experiments we describe the range of time-to-maturity and moneyness for which the approximation is accurate. We further propose a simple calibration procedure of an arbitrary parametric model to short-term near-the-money implied volatilities. An important advantage of our approximation is that it is free of the unobserved spot volatility. Therefore, the model can be calibrated on option data pooled across different calendar dates in order to extract information from the dynamics of the implied volatility smile. An example of calibration to a sample of S&P500 option prices is provided. We find that jumps are significant. The evidence also supports an affine specification for the jump intensity and Constant-Elasticity-of-Variance for the dynamics of the return volatility.

Online forums provide rich environments where users may post questions and comments about different topics. Understanding how people behave in online forums may shed light on the fundamental mechanisms by which collective thinking emerges in a group of individuals, but it has also important practical applications, for instance to improve user experience, increase engagement or automatically identify bullying. Importantly, the datasets generated by the activity of the users are often openly available for researchers, in contrast to other sources of data in computational social science. In this survey, we map the main research directions that arose in recent years and focus primarily on the most popular platform, Reddit. We distinguish and categorise research depending on their focus on the posts or on the users, and point to different types of methodologies to extract information from the structure and dynamics of the system. We emphasize the diversity and richness of the research in terms of questions and methods, and suggest future avenues of research.

Internet boards are platforms for online discussions about a variety of topics. On these boards, individuals may start a new thread on a specific matter, or leave comments in an existing discussion. The resulting collective process leads to the formation of 'discussion trees', where nodes represent a post and comments, and an edge represents a 'reply-to' relation. The structure of discussion trees has been analysed in previous works, but only from a static perspective. In this paper, we focus on their structural and dynamical properties by modelling their formation as a self-exciting Hawkes process. We first study a Reddit dataset to show that the structure of the trees resemble those produced by a Galton-Watson process with a special root offspring distribution. The dynamical aspect of the model is then used to predict future commenting activity and the final size of a discussion tree. We compare the efficiency of our approach with previous works and show its superiority for the prediction of the dynamics of discussion.