An Economic Bubble Model and Its First Hitting Time

We introduce a new diffusion process $X_t$ to describe asset price dynamics within an economic bubble cycle. The main feature in our model is the special drift term where the dependence structure among the price, the... [ view full abstract ]

We introduce a new diffusion process $X_t$ to describe asset price dynamics within an economic bubble cycle. The main feature in our model is the special drift term where the dependence structure among the price, the instantaneous return and the mean-reversion rate are mitigated. Our theoretical works show that both $X_t$ and its first hitting time are well-defined; calibration scheme and related probabilities are provided for application. Numerical examples illustrate the applications in 2000 dot-com bubble and 2007 Chinese stock market crash. In the end a prediction on BitCoin price has been given.