A discrete trinomial model for the birth and death of stock financial bubbles

The present work proposes a novel way to model the dynamic of financial bubbles. In particular we exploit the so called trinomial tree technique, which is mainly inspired by the typical market order book (MOB) structure. According to the typical MOB rules, we exploit a bottom-up approach to derive the relevant generator process for the financial quantities characterizing the market we are considering. Our proposal pays attention in considering the real world changes in probability levels characterizing the bid-ask preferences, focusing the attention on the market movements. In particular, we show that financial bubbles are originated by these movements which also act amplify their growth.