Extent3 prognoz practical_approach_lppl_model_2012

About Prognoz

Leading Russian developers of Business Intelligence

and Performance Management systems

• international company that has

been working in the IT market

since 1991

• joint team of over 1 200 skilled

economists, programmers,

analysts

• 50% market of BI in Russia

• Prognoz Platform, 1-st Russian

platform in Magic Quadrant of

Gartner

About MMP cluster

MMP cluster architecture

Historical bubbles

Definition of financial bubbles

Evolution of bubble and risk management

Monitoring of financial bubbles

The system of bubble recognition

LPPL model

Fitting of the model

Models selection

Financial bubble experiment

Market microstructure approach

Technical architecture

Financial bubbles

Theory of crashes

Practical approach

Science and experiment

3

CONTENTS

Financial engineering

(Stylized facts)

……………………………………….…................…

Liquidity of the financial market and

assets

……………………………………………………….…..

Agent-based modeling and simulation

……………………………………………………………

Market microstructure analysis

…………………………..………………………………

Bubble detection and diagnosis

……………………………………………………………

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Installation Site: Perm state university

Supercomputer type: Cluster

Number of nodes: 3

Number of Cores per node: 12

CPU type: Intel Xeon 5650 (2.66 GHz)

RAM per node: 64 Gb

OS: Windows Server 2003

Technical info:

Total: 48 services, 72 CPU, 228 Gb RAM

6

R is statistical and graphical

programming environment

Appeared in 1993 and designed by

Ross Ihaka and Robert Gentleman

R is a GNU project

R – a free implementation of the S

language

It runs on a variety of platforms

including Windows, Unix and MacOS

It contains advanced statistical

routines not yet available in other

packages

There is more than 4300

packages that allow to use

specialized statistical

techniques, graphical

devices, import/export

capabilities, reporting tools,

etc.

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Database

Commands

Batch file R file

Batch file

Batch file

R file

R file

Task

Runner

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Thefreedictionary.com

Mr. Greenspan

Charles Kindleberger, MIT

Professor J.Barley Rosser, James Madison University

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Authors A.Johansen, O.Ledoit, D.Sornette (JLS)

First publication Large financial crashes (1997) Famous book Didier Sornette Why Stock Markets Crash (2004)

𝑡𝑐 - critical time when bubble crash or change to another regime

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𝑙𝑛 𝑝 𝑡 = 𝐴 + 𝐵(𝑡𝑐 − 𝑡)𝑚

𝑡𝑐

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𝐶(𝑡𝑐 − 𝑡)𝑚 𝑐𝑜𝑠 [𝜔 𝑙𝑜𝑔 𝑡𝑐 − 𝑡 − 𝜑]

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𝑙𝑛 𝑝 𝑡 = 𝐴 + 𝐵(𝑡𝑐 − 𝑡)𝑚+𝐶(𝑡𝑐 − 𝑡)𝑚 𝑐𝑜𝑠 [𝜔 𝑙𝑜𝑔 𝑡𝑐 − 𝑡 − 𝜑]

m = 0.3 m = 0.01

m = 0.9 m = 1.7

𝑙𝑛 𝑝 𝑡 = 𝐴 + 𝐵(𝑡𝑐 − 𝑡)𝑚+𝐶(𝑡𝑐 − 𝑡)𝑚 𝑐𝑜𝑠 [𝜔 𝑙𝑜𝑔 𝑡𝑐 − 𝑡 − 𝜑]

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𝑙𝑛 [𝑝(𝑡)]

= 3 = 7

= 30 = 15

𝑙𝑛 𝑝 𝑡 = 𝐴 + 𝐵(𝑡𝑐 − 𝑡)𝑚+𝐶(𝑡𝑐 − 𝑡)𝑚 𝑐𝑜𝑠 [𝜔 𝑙𝑜𝑔 𝑡𝑐 − 𝑡 − 𝜑]

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𝑡𝑐 − 𝑡

𝑡𝑐 − 𝑡

𝑡𝑐 − 𝑡 𝑡𝑐 − 𝑡

𝑡𝑐 − 𝑡

= 7 = 9.5

𝑙𝑛 𝑝 𝑡 = 𝐴 + 𝐵(𝑡𝑐 − 𝑡)𝑚+𝐶(𝑡𝑐 − 𝑡)𝑚 𝑐𝑜𝑠 [𝜔 𝑙𝑜𝑔 𝑡𝑐 − 𝑡 − 𝜑]

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For each log periodic curve we fixed:

𝑡0- start time of the bubble 𝑡𝑐 - critical time when bubble crash or change to another regime

𝑡𝑐1 𝑡𝑐2

Sample of 𝑡𝑐

First model

Second model

John von Neumann

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• Main filtration (0<m<1, B<0)

• Residuals stationarity tests (ADF test, Phillips–Perron test)

• Lomb spectral analysis

0 10 20 30 40

05

01

00

15

0

LOMB PERIODOGRAM

omega

P(o

me

ga

)

m

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Risk measure

Quantiles

Distribution of 𝑡𝑐

Sample of 𝑡𝑐

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D.Fantazzini, P.Geraskin,

Everything You Always Wanted to Know

about Log Periodic Power Laws for Bubble Modelling

but Were Afraid to Ask (2011)

• Bubble

• Anti - bubble

Type

• Long

• Short

Timeframe

• Large

• Small

Size

• Parameters

LPPL

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The Financial Crisis Observatory (FCO) is a scientific platform aimed at testing and

quantifying rigorously, in a systematic way and on a large scale the hypothesis that

financial markets exhibit a degree of inefficiency and a potential for predictability,

especially during regimes when bubbles develop. (http://www.er.ethz.ch/fco/index)

Testing two hypotheses:

• Hypothesis H1: financial (and other) bubbles can be diagnosed in real-time

before they end..

• Hypothesis H2: The termination of financial (and other) bubbles can be

bracketed using probabilistic forecasts, with a reliability better than chance

(which remains to be quantied).

D. Sornette, R. Woodard,

M. Fedorovsky,S. Reimann, H. Woodard, W.-X. Zhou

The Financial Bubble Experiment. First Results (2 November 2009 - 1 May 2010)

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2 November 2009 – 1 May 2010 [http://www.er.ethz.ch/fco/FBE_report_May_2010]

2 of 4 bubbles detected by model were real bubbles

All of them changed their regimes

12 May 2010 – 1 November 2010 [http://www.er.ethz.ch/fco/fbe_Report_1Nov10_2]

5 of 7 bubbles detected by model were real bubbles

4 of 5 changed their regimes

12 November 2011 – 2 May 2011 [http://www.er.ethz.ch/fco/fbe_20110502_assets_3.pdf]

24 of 27 bubbles detected by model were real bubbles

17 of 24 changed there regime

NBER Working Group

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Different types of filters at 3 time scales:

Hours scale (macro):

Absolute filter

Relative filter

Source: Guo-Hua Mu, Wei-Xing Zhou, Wei Chen and J´anos Kert´esz. Order flow dynamics around extreme price changes on an emerging stock market, 2010

Minutes scale (meso):

Filter of minute returns

Source: Armand Joulin, Augustin Lefevre, Daniel Grunberg, Jean-Philippe Bouchaud. Stock price jumps: news and volume play a minor role, 2010

Tick scale (micro):

NANEX filter

Source: Flash Crash Analysis Continuing Developments http://www.nanex.net/FlashCrashEquities/FlashCrashAnalysis_Equities.html

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pri

ce [r

ub

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time [ticks]

1.775

1.785

1.795

1.805

1.815

1.825

1.835

1.845

1.855

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ce, r

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time

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pri

ce [r

ub

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time [ticks]

Within 1 second price rose 0.82 % for 16 ticks (61.2 ->61.7)

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Stocks analyzed 29 blue chips

Period 01.04.2010-30.06.2010; 1.09.2010-12.10.2010

Trading days 82

Sample analyzed 20.2 mln. ticks

Trading time 11.30-18.40

Shocks found 369

IDENT UP DOWN ALL PMTL 15 36 51 MAGN 31 6 37 NOTK 18 18 36 OGKC 13 23 36 AFLT 9 25 34 RTKM 14 19 33 MGNT 4 16 20 NLMK 8 12 20 URKA 7 11 18 SIBN 6 10 16 RASP 7 8 15 MRKH 3 9 12 MSNG 5 7 12 CHMF 3 4 7 RU14TATN3006 3 3 6 HYDR 3 2 5 TRNFP 3 0 3 IUES 0 2 2 MTSI 1 1 2 SNGSP 2 0 2 ROSN 1 0 1 SNGS 1 0 1 FEES 0 0 0 GAZP 0 0 0 GMKN 0 0 0 LKOH 0 0 0 SBER03 0 0 0 SBERP03 0 0 0 VTBR 0 0 0 Average 5 7 13

Total 369 events (13 per stock) On average 1 shock/7 days per stock

We use a tick dynamics of prices for filtering (source: MICEX)

Statistics:

Science

Laboratory of financial modeling and risk

management - Prognoz Risk Lab

Мagistracy in finance and IT (Master in

Finance & IT) in Perm State National Research

University

mifit.ru

Perm Winter School is an annual conference

on modeling of financial markets and risk

management

permwinterschool.ru