本研究基于对数周期幂律模型LPPL（Log Periodic Power Law Model），针对金融时间序列将一维价格波动翻译成反映市场泡沫微观结构的多维变量。通过对多维变量的动态监测，把握市场中泡沫的演变并预测泡沫破裂的临界点，从而有效降低或防范金融资产泡沫破裂所导致的风险。为检验LPPL模型在中国金融市场中的适用性，本文分别使用上证综指、四个期货连续合约以及两支个股检验模型效果。实证结果表明当金融资产价格序列呈现超指数加速震荡上升或下降时，该模型能获得稳定的估计效果，有效预测泡沫破裂临界时点。
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(tc-t)m{1+Ccos(ωln(tc-t)-φ)}
where lnp(t) is the logarithm of index or assets price.tc 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.
[1] Johansen A, Sornette D.Critical crashes[J]. Risk, 1999, 12(1):91-94.
[2] Zhou Weixing, Sornette D. Analysis of the real estatemarket in Las Vegas:Bubble,seasonal patterns, and prediction of the CSW indices[J].Physica A:Statistical Mechanics and Its Applications,2008(387):243-260.
[3] Sornette D. Why stock market crash:Critical events in complex financial systems[M].Princeton:Princeton University Press,2003.
[4] Zhou Weixing, Sornette D. 2000-2003 real estate bubblein the UK but not in the USA[J]. Physica A:Statistical Mechanics and Its Applications,2003(329):249-263.
[5] Johansen A, Sornette D. Endogenous versus exogenous crashes in financial market[J]. International Journal of Theoretical and Applied Finance, 2002,(6):643-730.
[6] Zhang Qunzhi, Sornette D, Balcilar M, et al. LPPLS bubble indicators over two centuries of the S&P 500index[J]. Physica A:Statistical Mechanics and Its Applications, 2016,(458):126-139.
[7] Sornette D, Woodard R, Yan Wanfeng, et al. Clarifications to questions and criticisms on the Johansen-Ledoit-Sornette financial bubble model[J]. Physica A:Statistical Mechanics and Its Applications, 2013,(392):4417-4428.
[8] Li Chong. Log-periodic view on critical dates of the Chinese stockmarket bubbles[J]. Physica A:Statistical Mechanics and Its Applications, 2017(465):305-311.
[9] De Long J B, Shleifer A, Summers L H,et al. Noise trader risk in financial markets[J].Journal of Political Economy, 1990,98(4):703-738.
[10] 温红梅,姚凤阁.我国房地产市场价格泡沫的实证分析——以北京地区为例[J].中国管理科学,2007,15(S1):280-285.
[11] 李东.LPPL模型算法的初步探讨[J].淮海工学院学报(自然科学版),2012, 21(3):4-7.
[12] 周伟,何建敏.后危机时代金属期货价格集体上涨——市场需求还是投机泡沫[J].金融研究,2011,(9):65-77.
[13] 方勇.中国股票市场自组织临界性与对数周期幂律的实证研究[J].统计与决策,2011,(10):36-38.
[14] 徐浩峰,朱松.机构投资者与股市泡沫的形成[J].中国管理科学,2012,20(4):18-26.
[15] 吉翔,高英.中国股市的泡沫与反泡沫——基于对数周期性幂律模型的实证研究[J].山西财经大学学报,2012,(12):27-38.
[16] 扈文秀,刘刚,章伟果,等.基于因素嵌入的非理性资产价格泡沫生成及膨胀演化研究[J].中国管理科学,2016,24(5):31-37.
[17] 石建勋,王盼盼,何宗武.中国牛市真的是"水牛"吗?——不确定性视角下股市价量关系的实证研究[J].中国管理科学,2017, 25(9):71-80.
[18] 陈卫华,蔡文靖.基于LPPL模型的股市暴跌风险预警[J],统计与决策,2018,(5):143-146.
