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Financial bubble diagnostics
based on log-periodic power law
model

Perm State National Research
University

Perm R group
...
About financial bubbles
It was very difficult to definitively identify a bubble
until after the fact—that is, when it is bur...
3

Tulipomania
• 1585 – 1650 Netherlands
• Creating futures and options on the tulips
• The fall is 100 times
4

Crash 1929. Dow Jones
5

The crisis in October 1987. S&P 500
6

The crisis in October 1997. Index Hang Seng
7

The collapse of the RTS in 1997
8

Crash of index NASDAQ in 2000
Crash of index Dow Jones. 2007
Crash of index RTS in 2008
11

What is common???
12

Log Periodic Power Law (LPPL)
Authors
A.Johansen, O.Ledoit, D.Sornette (JLS)

First publication
Large financial crashe...
13

Power law?
14

Log Periodic ?
15

LPPL = log periodic + power law
What is m?

m = 0.01

m = 0.9

m = 0.3

m = 1.7

16
What is ?

=3

=7

= 15

= 30

17
What is ?

=7

= 9.5

18
Critical time estimation
First model

Second model

19
With four parameters I can fit an
elephant, and with five I can make
him wiggle his trunk.
John von Neumann

20
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

Estimation of parameters
• Splitting the tolerance values ​on the grid

• Finding the grid parameters providing a mini...
23

Various sections of the cost function
24

New method for estimating the parameters

V.Filimonov and D.Sornette
A Stable and Robust Calibration Scheme
of the Log...
25

New method for estimating the parameters
26

The most important results

•
27

Various sections of the cost function after transformation
28

Estimation of parameters

t0
tc

m
The procedure for estimation
of parameters

B

ln[ p(t )]

A

Filter
Models selection

•

150

LOMB PERIODOGRAM

0

50

P(omega)

100

m

0

10

20
omega

30

40

29
30

Lomb spectral analysis
31

The evolution of the bubble …
32

The Crash Lock-In Plot (CLIP)

D.Fantazzini, P.Geraskin,
Everything You Always Wanted to Know
about Log Periodic Power...
33
34
The practical task № 6. Estimate LPPL model
TASK :
a. Download Nikkei Index Data(ticker: “^N225”) from June 2012 to June 2...
Q&A

arbuzov@prognoz.ru
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Seminar psu 21.10.2013 financial bubble diagnostics based on log-periodic power law model

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Seminar psu 21.10.2013 financial bubble diagnostics based on log-periodic power law model

  1. 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. 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. 3 Tulipomania • 1585 – 1650 Netherlands • Creating futures and options on the tulips • The fall is 100 times
  4. 4. 4 Crash 1929. Dow Jones
  5. 5. 5 The crisis in October 1987. S&P 500
  6. 6. 6 The crisis in October 1997. Index Hang Seng
  7. 7. 7 The collapse of the RTS in 1997
  8. 8. 8 Crash of index NASDAQ in 2000
  9. 9. Crash of index Dow Jones. 2007
  10. 10. Crash of index RTS in 2008
  11. 11. 11 What is common???
  12. 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. 13 Power law?
  14. 14. 14 Log Periodic ?
  15. 15. 15 LPPL = log periodic + power law
  16. 16. What is m? m = 0.01 m = 0.9 m = 0.3 m = 1.7 16
  17. 17. What is ? =3 =7 = 15 = 30 17
  18. 18. What is ? =7 = 9.5 18
  19. 19. Critical time estimation First model Second model 19
  20. 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. 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. 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. 23 Various sections of the cost function
  24. 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. 25 New method for estimating the parameters
  26. 26. 26 The most important results •
  27. 27. 27 Various sections of the cost function after transformation
  28. 28. 28 Estimation of parameters t0 tc m The procedure for estimation of parameters B ln[ p(t )] A Filter
  29. 29. Models selection • 150 LOMB PERIODOGRAM 0 50 P(omega) 100 m 0 10 20 omega 30 40 29
  30. 30. 30 Lomb spectral analysis
  31. 31. 31 The evolution of the bubble …
  32. 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. 33
  34. 34. 34
  35. 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. 36. Q&A arbuzov@prognoz.ru

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