In this paper, we draw upon the close relationship between statistical physics and mathematical finance to develop a suite of models for financial bubbles and crashes. By modifying previous approaches, we are able to derive novel analytical formulae for evaluation problems and for the expected...

High-frequency financial data are characterized by a set of ubiquitous statistical properties that prevail with surprising uniformity. While these 'stylized facts' have been well-known for decades, attempts at their behavioral explanation have remained scarce. However, recently a new branch of...

High-frequency financial data are characterized by a set of ubiquitous statistical properties that prevail with surprising uniformity. While these 'stylized facts' have been well-known for decades, attempts at their behavioral explanation have remained scarce. However, recently a new branch of...

We overview different methods of modeling volatility of stock prices and exchange rates, focusing on their ability to reproduce the empirical properties in the corresponding time series. The properties of price fluctuations vary across the time scales of observation. The adequacy of different...