Testing Of The LPPL Model On Real World Financial Bubbles And Market Crashes

There are bubbles in the financial markets periodically, and eventually the bubbleswill probably lead to market crashes which will cause severe damage to economic andsocial developments. Using mathematical methods to model and study financialbubbles and market crashes has great meanings in more deeply understand the bubbleand the crash and in preventing the damages caused by market crashes. In the meantime,studying the market bubbles can be very helpful to the investors who trade on themarkets.The research in this paper is based on the Log Periodic Power Law model to studythe financial bubble data before the market crashes. By defining the start of the bubbleand defining the top of the bubble, this paper fits the Hang Seng Index data before eachbubble to the LPPL model, and the study the value of the key parameters in the fit. Bydiscussing the range of the values of the key parameters, the paper try to give estimateand predictions on the critical crash time of the financial bubbles.At the same time this paper conducts tests on the very early theories the otherresearchers did on the LPPL model in order to point out the inadequacy of their work,and then the last part of the paper try to give some suggestions and supplements to theirwork.