Stock Financial Bubbles: a trinomial trees based analysis

In the present work we consider a novel approach to model the dynamic of financial bubbles. In particular, we exploit a technique based on trinomial trees, which is mainly inspired by the typical Market Order Book (MOB) structure. We use a bottom-up approach, according to the typical MOB rules, to derive the relevant generator process for the financial quantities characterizing the market we are considering. Our proposal pays specific attention to consider the real world changes in probability levels characterizing the bid- ask preferences driven by market movements. We show that financial bubbles are, indeed, originated by these movements which, in turn, amplify their growth. Numerical experiments are provided to show the effectiveness of our results within real volatility wars scenarios. Namely, we study realistic economic frameworks characterized by volatility levels showing great fluctuations, in relatively small times.