A Stochastic Tree for Bubble Asset Modelling and Pricing

We introduce a new stochastic tree representation of a strictly stationary submartingale process for modelling, forecasting, and pricing speculative bubbles on commodity and cryptocurrency markets. The model is compared to other trees proposed in the literature on bubble asset modelling and stochastic volatility approximation. We show that the proposed model is an extension of the well-known Blanchard-Watson bubble. The model provides (quasi) closed-form pricing formulas for European options, which are derived and illustrated.