Abstract: This paper focus on the financial bubbles crash by establishing the Log Periodic Power Law Model, which translates one-dimensional price fluctuations of the financial time series into multidimensional variables reflecting the market microstructure about the bubbles. The Log Periodic Power Law Model is very useful to characterize the formation and crash of the financial bubbles. The LPPL model is:
lnp(t)=A+B(t_c-t)^m{1+Ccos(ωln(t_c-t)-φ)}
where lnp(t) is the logarithm of index or assets price.t_c is the critical point of bubble burst. The least square method is applied to estimate parameters in the model, and using Nelder-Mead Simplex algorithm is used for finding the optimal parameters. Dynamic detecting the multidimensional variables, diagnosing bubbles that are in the making and to forecast their termination time, so as to effectively reduce or prevent the financial risk from the financial bubbles crashing. The Shanghai Composite Index, four futures contracts and two stocks are performed on, for testing the applicability of LPPL Model in the financial market of China. The empirical results show that when the financial asset price series presents hyper exponential acceleration, shocks rise or fall, the model modified can be used to obtain a stable estimation, and effectively predict the critical point of the bubble burst. This paper not only tests the validity of LPPL model based on China financial market, but also provides a powerful tool for detecting financial bubbles or forecasting the bubbles crash. Moreover, as a supplementary guide for trading strategies.

Key words: Log Periodic Power Law Model, bubble crash, hyperexponential, critical point