1. Financial bubble diagnostics
based on log-periodic power law
model
Perm State National Research
University
Perm R group
r-group.mifit.ru
ITE.LAB “MathEconomics” Open Course
Russia, Perm, 21 November 2013
Arbuzov V.
arbuzov@prognoz.ru

2. About financial bubbles
It was very difficult to definitively identify a bubble
until after the fact—that is, when it is bursting we confirm its existence.
Mr. Greenspan
A situation in which prices for securities, especially stocks, rise far above their
actual value. This trend continues until investors realize just how far prices have
risen, usually, but not always, resulting in a sharp decline.
Thefreedictionary.com
An upward price movement over an extended range that then implodes.
Charles Kindleberger, MIT
A speculative bubble exists when the price of something does not equal its market
fundamentals for some period of time for reasons other than random shocks.
Professor J.Barley Rosser, James Madison University
2

3. 3
Tulipomania
• 1585 – 1650 Netherlands
• Creating futures and options on the tulips
• The fall is 100 times

4. 4
Crash 1929. Dow Jones

5. 5
The crisis in October 1987. S&P 500

6. 6
The crisis in October 1997. Index Hang Seng

7. 7
The collapse of the RTS in 1997

8. 8
Crash of index NASDAQ in 2000

9. Crash of index Dow Jones. 2007

10. Crash of index RTS in 2008

11. 11
What is common???

12. 12
Log Periodic Power Law (LPPL)
Authors
A.Johansen, O.Ledoit, D.Sornette (JLS)
First publication
Large financial crashes (1997)
Famous book
Didier Sornette
Why Stock Markets Crash (2004)

13. 13
Power law?

14. 14
Log Periodic ?

15. 15
LPPL = log periodic + power law

16. What is m?
m = 0.01
m = 0.9
m = 0.3
m = 1.7
16

17. What is ?
=3
=7
= 15
= 30
17

18. What is ?
=7
= 9.5
18

19. Critical time estimation
First model
Second model
19

20. With four parameters I can fit an
elephant, and with five I can make
him wiggle his trunk.
John von Neumann
20

21. 21
Estimation of parameters
A
B
C
N
fi
gi
fi
fi 2
f i gi
gi
gi f i
gi2
1
ln pi
ln pi fi
ln pi gi

22. 22
Estimation of parameters
• Splitting the tolerance values ​on the grid
• Finding the grid parameters providing a minimum sum of squared
residuals
• Optimizing found on the grid parameters using the Newton-Gauss

23. 23
Various sections of the cost function

24. 24
New method for estimating the parameters
V.Filimonov and D.Sornette
A Stable and Robust Calibration Scheme
of the Log-Periodic Power Law Model
(29 aug 2011)

25. 25
New method for estimating the parameters

26. 26
The most important results
•

27. 27
Various sections of the cost function after transformation

28. 28
Estimation of parameters
t0
tc
m
The procedure for estimation
of parameters
B
ln[ p(t )]
A
Filter

29. Models selection
•
150
LOMB PERIODOGRAM
0
50
P(omega)
100
m
0
10
20
omega
30
40
29

30. 30
Lomb spectral analysis

31. 31
The evolution of the bubble …

32. 32
The Crash Lock-In Plot (CLIP)
D.Fantazzini, P.Geraskin,
Everything You Always Wanted to Know
about Log Periodic Power
Laws for Bubble Modelling but Were Afraid to Ask (2011)

33. 33

34. 34

35. The practical task № 6. Estimate LPPL model
TASK :
a. Download Nikkei Index Data(ticker: “^N225”) from June 2012 to June 2013
b. Estimate parameters of model LPPL
MODEL LPPL:
Commands to help :
help(nsl)

36. Q&A
arbuzov@prognoz.ru