Presentation Etalon12 12 Last

Financial market crises predictionFinancial market crises prediction by multifractal and wavelet by multifractal and wavelet

analysis.analysis.

Russian Plekhanov Academy of EconomicsRussian Plekhanov Academy of Economics

Romanov V.P., Bachinin Y.G., Moskovoy I.N., Badrina M.VRomanov V.P., Bachinin Y.G., Moskovoy I.N., Badrina M.V..

It is well known, that financial markets are essentially non-linear systems and financial time series are fractals.

That’s why prediction of crash situations at finance market is a very difficult task. It doesn’t allow us to use effectively such well-known methods as ARIMA or MACD in view of their sluggishness.

Multifractal and wavelets analysis methods are providing more deep insight into the nature of phenomena..

The main aim of this research is to find out the predictors or some kind of predicting signals, which may warn as about forthcoming crisis

The aim of the researchThe aim of the research

a) Changing of ruble/dollar exchange rate at period 01.08.1997-01.11.1999 (Default in Russia)

b) American Index Dow Jones Industrial at “Black Monday” 1987 at period 17.10.1986-31.12.1987

с) Dow Jones Industrial Index

e) Nasdaq

d) RTSI

07.10.1999 -06.10.2008

07.10.1999 -06.10.2008

07.10.1999 -06.10.2008

Efficient Market Hypothesis (EMH) asserts, that financial markets are "informationally efficient", or that prices on traded assets, e.g., stocks, bonds, or property, already reflect all known information. The efficient-market hypothesis states that it is impossible to consistently outperform the market by using any information that the market already knows, except through luck. Information or news in the EMH is defined as anything that may affect prices that is unknowable in the present and thus appears randomly in the future.

Capital Asset Pricing Model (CAPM) is used to determine a theoretically appropriate required rate of return of an asset, if that asset is to be added to an already well-diversified portfolio, given that asset's non-diversifiable risk. The model takes into account the asset's sensitivity to non-diversifiable risk (also known as systemic risk or market risk), often represented by the quantity beta (β) in the financial industry, as well as the expected return of the market and the expected return of a theoretical risk-free asset.

Arbitrage pricing theory (APT), in finance, is a general theory of asset pricing, that has become influential in the pricing of stocks. APT holds that the expected return of a financial asset can be modeled as a linear function of various macro-economic factors or theoretical market indices, where sensitivity to changes in each factor is represented by a factor-specific beta coefficient.

Efficient Market HypothesisEfficient Market Hypothesis versusversus Fractal Market HypothesisFractal Market Hypothesis

Efficient market hypothesysEfficient market hypothesys ((EMHEMH))

Assumption of normal distribution of prices increments

The weak form of EMH from a purely random distribution of prices has been criticized

Semi-strong form of EMH, in which all available information is reflected in the prices used by professionals

Changing prices in the long run does not show the presence of «memory»

Fractral market hypothesysFractral market hypothesys(FMH)

Prices shows leptoexcess effect for prices probability distribution(“fat tails”)

The prices plot looks similary for the period of time in the day, week, month (fractal pattern)

Reducing the reliability of predictions with the increase of its period

Prices shows short-term and long-term correlation and trends (the effect of feedback)

Chaotic activity of the market

• FractalsFractals – –The term fractal was introduced in 1975 by Benoît Mandelbrot, from the Latin fractus, meaning "broken" or "fractured".• A shape that is recursively constructed or self-similar, that is, a shape that appears similar at all scales of magnification.• A geometric object that has a Hausdorff dimension greater than its topological dimension.• The second feature that characterizes fractals is the fractional dimension.• The word fractal came from “fractional values” – partial values, which may take the fractal dimension of objects

Fractal definitionFractal definition

Chaos and dynamics of fractal marketChaos and dynamics of fractal market

Market prices tend to level the natural balance within the price range

These levels or ranges can be described as «attractors»

However, the data within those ranges remain casual

Fractal attractors andFractal attractors and financial markets financial markets

Stocks and futures - classic examples of securities. Profit from buying and selling comparable with fluctuations in the pendulum

Each security or futures contract are located in its own phase space

Long-term forecasting is heavily dependent on accurate measurement of initial conditions of the market

Fractals on capital marketFractals on capital market Financial markets describes a

nonlinear function of active traders

Traditional methods of technical analysis based on linear equations and Euclidean geometry are inadequate

Market jumps growth and recession are nonlinear

Technical analysis methods are poor indicators of the relationship trend and trading decisions

Fractals can describe the phenomena that are not described in Euclidean geometry

Point attractorsPoint attractors

• The simplest form of the attractor. In theory, compatible with the balance of supply and demand in the economy or the market equilibrium.

• Represent market volatility on balance, or "market waves"

• Displays multiple chaotic,varying the amplitude fluctuation, which are contained within the set limit cycle attractor, called «phase space».

Limit cycle attractorsLimit cycle attractors

Strange or fractal attractorsStrange or fractal attractors

Attractors typesAttractors types

Serpinsky TriangleSerpinsky Triangle

Fractals examplesFractals examples

April 13, 2023 14

Dynamic systems fractals

Crisis prediction techniqueCrisis prediction technique

Because our goal is the prediction of crises, we are Because our goal is the prediction of crises, we are trying to first find out the best indicator, using trying to first find out the best indicator, using methodologies of fractal, multifractal and wavelet methodologies of fractal, multifractal and wavelet analysis.analysis.

First of all we looking for several different predictorsFirst of all we looking for several different predictors

Then we test various types of pre-processing the Then we test various types of pre-processing the original time series to find the best indicator.original time series to find the best indicator.

Definition the Fractal DimensionDefinition the Fractal Dimension

Fractal dimension :Fractal dimension :

wherewhere NNAA (1/(1/nn) –) – the number of blocks with length of the sided the number of blocks with length of the sided, ,

equalsequals 1/ 1/nn, , which necessary to coverwhich necessary to cover a set a set А.А. For S For S – – Serpinsky triangle:Serpinsky triangle: 58,1

)2ln(

)3ln(

)2ln(

)3ln(lim n

n

nsd

)ln(

))/1(ln(lim

n

nNd A

n

Hurst exponent (H) as one of predictorsHurst exponent (H) as one of predictors

Depending on the value of Heurst Depending on the value of Heurst exponent the properties of the exponent the properties of the process are distinguished as follows:process are distinguished as follows: When H = 0.5, there is a process of When H = 0.5, there is a process of random walks, which confirms the random walks, which confirms the hypothesis EMH. hypothesis EMH.

When H > 0.5, the process has long-When H > 0.5, the process has long-term memory and is persistent, that term memory and is persistent, that is it has a positive correlation for is it has a positive correlation for different time scales. different time scales.

When H < 0.5, time-series is anti-When H < 0.5, time-series is anti-persistent with average switching persistent with average switching from time to time.from time to time.

Ttzzx ttt ,...,1,lnln 1

11

1,),(

t

t

uu xxxxtx

),(min),(max)(11

txtxRtt

1

21)(

uu xxS

log)(

)(log SR

H

Fractal Dimension Index(FDI = 2-H)Fractal Dimension Index(FDI = 2-H)

Defines the persistence or antipersistence of Defines the persistence or antipersistence of market. Persistent market weakly fluctuated market. Persistent market weakly fluctuated around the market trend around the market trend

Antipersistent market shows considerable volatility Antipersistent market shows considerable volatility on the trend on the trend

Antipersistent market is more rugged pricing Antipersistent market is more rugged pricing schedule and more frequently show a change schedule and more frequently show a change trendstrends

Stochastic process {x(t)} is called Multifractal, if it has stationary increments and satisfies the condition

,

when c(q) – predictor, E- operator of mathematical expectation, , – intervals on the real axis.

Scaling function , which takes into account the impact of the time on the moments q.

Multifractal spectrum of singularityMultifractal spectrum of singularityas the second predictoras the second predictor

Qq

)(q

Bt

1τ(q)qtΔt+t tΔc(q)(=)|xxE(| )

.Multifractal spectrum of singularity Multifractal spectrum of singularity is defined by Legendre transform:

)]([minarg)( qqfq

Multifractal spectrum of singularity Multifractal spectrum of singularity width as crash indicatorwidth as crash indicator

Multifractal may be composed of two or infinite number of monofractals with continuous varying α values. Width of α spectrum may be estimated as difference between maximum and minimum values of α:

Δ = max - min , By carrying out Legendre transform we are trying

using our program by estimating Δ to find differences in its values before and after crash.

Roughly speaking f() gives us number of time moments, for which degree of polynomial, needed for approximation f() equals (according to Lipshitz condition).

Five steps Five steps of multifractal spectrum of singularity of multifractal spectrum of singularity estimation: estimation: The First step: The First step: time series partitioningtime series partitioning

Time series: {xt}; t [0, T].

Compute: Z={zt}, zt= lnxt+1-lnxt; t [0,T];

Divide interval [0, T] into N subintervals, 1 ≤ N ≤ Nmax.

Each subinterval contains int (T/N)=A values Z;

For each subinterval K; 1 ≤ K ≤ N current reading number lK;1 ≤ lK ≤ A; t = (K-1) А+ lK

As soon as we are looking for the best indicator of a coming default, we will use several variants of a preliminary processing.

The second step:The second step:Time series Time series preprocessingpreprocessing

1. The original time series itself: Z={zt};

2. Preprocessed time series Z1={ }, K=1,2,…N,

where

3. Preprocessed time series

where

4. Preprocessed time series Z3={ }

ZK

A

llK

K

Kz

AZ

10

1

K

KlAK

S

ZZZ K

10

2

A

lKlK

K

KZZ

AS

1

2

0

1

KlAK ZZK

10

The third step: The third step: Partition functions Partition functions computingcomputing

For each preprocessed time series compute partition function for different N and q values :

N

K

q

AKKAN ZTZqZ1

)1(0)(00 |)(|),(

N

K

qKKN ZTZqZ

11

1 |)(|),(

N

K

qAKN ZKAZqZ

1

)1(222 |)(|),(

N

K

q

AKKAN ZZqZ1

)1(3)(33 ||),(

The fourth step: The fourth step: Scaling function Scaling function computingcomputing

A

NAqZq

NN log

loglog),(log)(

00

A

NAqZq

NN log

loglog),(log)(

11

A

NAqZq

NN log

loglog),(log)(

22

A

NAqZq

NN log

loglog),(log)(

33

The fifth step: The fifth step: Multifractal spectrum Multifractal spectrum of singularity of singularity estimationestimation

1. Lipshitz – Hoelder exponent estimation: :

where, i = 1, 2, 3, 4.2. Multifractal spectrum of singularity Multifractal spectrum of singularity estimation by Legendre

transform

qqqqqdq

d iiii

i

/)(/))1()((

)])()([min(arg)]([minarg)( qqqqqf iiq

iq

I

Scaling functionScaling function

Non-linear scaling functionNon-linear scaling function(q) (q) ((Multifractal processMultifractal process))

Changes in currency for the Changes in currency for the Russian default of 1998Russian default of 1998

Multifractal spectrum of singularity at period 09.07.96-

21.07.98

Multifractal spectrum of singularity at period 18.11.96-

30.11.98

Multifractal spectrum of singularityMultifractal spectrum of singularity

Dow Jones Industrial Index, pre-crisis situation

19.12.2006-06.10.2008

Scaling functionsScaling functions

Non-linear scaling-function (q) (multifractal process)

RTSI index, pre-crisis situation

19.12.2006-06.10.2008

Non-linear scaling-function (q) (multifractal process)



linear scaling-function (q) (monofractal process)

Multifractal spectrum of singularity RTSI at period 16.05.2000 -30.05.2002

Multifractal spectrum of singularity Multifractal spectrum of singularity for analyzed situationsfor analyzed situations

Multifractal spectrum of singularity DJI at period 19.12.2006-08.10.2008

Multifractal spectrum of singularity RTSI at period

16.12.2003-10.01.2006

Russian default 1998 and USA Black Monday 1987 analysis

Plot of the august 1998 Russian default currency exchanging data

Plot of width of fractal dimension spectrum (Δ(t)=αmax-αmin) for different time periods

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Ряд1

US Dow Jones index for Black Monday 1987 for period 17.10.1986-31.12.1987

Plot of width of fractal dimension spectrum (Δ(t)=αmax-αmin) the Black Monday

0

0,10,2

0,30,4

0,50,6

one yearbeforedefolt

11.07.96-23.07.98

19.07.96-31.07.98

29.07.96-10.08.98

06.08.96-18.08.98

14.08.96-26.08.98

00,050,1

0,150,2

0,250,3

Indexes DJI, RTS.RS, NASDAQ,S&P 500 falling at 2008 crisis period

1 monthSeptember 15,2008 – October 17, 2008

The collapse in the stock markets the analysts linked to the negative external background. U.S. indexes have completed a week 29.09 - 6.10 falling, despite the fact that the U.S. Congress approved a plan to rescue the economy.

Investors fear that the attempt to improve the situation by pouring in amount of $ 700 billion, which involves buying from banks illiquid assets will not be able to improve the situation in credit markets and prevent a decline in the economy.

3 months July 17,2008 – October 17, 2008

When Asian stock indices collapsed to a minimum for more than three years. The negative news had left the Russian market no choice – its began to decline rapidly.

6 months April 17,2008 – October 17, 2008

"Needles“, that determine the expansion of Multifractal "Needles“, that determine the expansion of Multifractal spectrum at hourly schedule spectrum at hourly schedule 5.2008-11.20085.2008-11.2008

Graph of Multifractal spectrum singularity width (Graph of Multifractal spectrum singularity width (ΔΔ(t)=(t)=ααmaxmax--ααminmin)) atat

Russian index RTSI at periodRussian index RTSI at period 0707.10.19.10.199999--0707.1.111..20082008

interval Qmin Qmax

N ∆

1-51207.10.1999 –18.10.2001

-2 6 47 0,964151-662

16.05.2000 -30.05.2002-2 6 103 0,495

301-81215.12.2000 -31.12.2002

-2 6 129 1,62451-962

25.07.2001 -11.08.2003-2 5 31 0,81

601-111228.02.2002 -17.03.2004

-2 6 170 1,77751-1262

03.10.2002 -19.10.2004-2 6 129 2,17

901- 141215.05.2003 -02.06.2005

-2 6 129 1,9271051-1562

16.12.2003 -10.01.2006-2 5 43 0,952

1201-171226.07.2004 -15.08.2006

-2 5 21 0,8681351-1862

04.03.2005 -26.03.2007-2 5 22 0,89

1501-201206.10.2005 -25.10.2007

-2 5 23 0,8481651-2162

19.05.2006 -07.06.2008-2 5 40 0,927

1801-224619.12.2006 -06.10.2008

-2 7 145 2,1331765-2277

25.09.2006 -07.11.2008-2 7 161 2,177

Experimental resultsExperimental results(RTSI)(RTSI)

Graph of Multifractal spectrum singularity width assessment (Δ(t)=αmax-αmin) at russian index RTSI at period 07.10.1999-07.11.2008

Over 4 years outstanding mortgage loans in Russia rose Over 4 years outstanding mortgage loans in Russia rose more than 16 times - from 3.6 billion rubles. in 2002 to 58.0 billion more than 16 times - from 3.6 billion rubles. in 2002 to 58.0 billion rubles. in 2005. In quantitative terms - from 9,000 loans in 2002 to rubles. in 2005. In quantitative terms - from 9,000 loans in 2002 to

78,603 in 2005.78,603 in 2005.

Why mortgage evolving so rapidly? Many factors. This increase in real Why mortgage evolving so rapidly? Many factors. This increase in real incomes and the decline of distrust towards mortgage, as from potential incomes and the decline of distrust towards mortgage, as from potential buyers, and from the sellers, and a general reduction in the average interest buyers, and from the sellers, and a general reduction in the average interest rate for mortgage loans from 14 to 11% per annum, and the advent of rate for mortgage loans from 14 to 11% per annum, and the advent of Moscow banks in the regions, and intensifying in the market of small and Moscow banks in the regions, and intensifying in the market of small and medium-sized banks.medium-sized banks.

Pre-crisis situation: Pre-crisis situation: July 2008 - the beginning of september 2008 July 2008 - the beginning of september 2008

Graph of Multifractal spectrum singularity width (Graph of Multifractal spectrum singularity width (ΔΔ(t)=(t)=ααmaxmax--ααminmin)) atat

Russian index RTSI at periodRussian index RTSI at period 0707.10.19.10.199999--0909.1.122..20082008

interval Qmin Qmax N ∆

1-51207.10.1999 –18.10.2001

-2 5 164 1,84151-662

16.05.2000 -30.05.2002-2 4 5 0,717

301-81215.12.2000 -31.12.2002

-2 5 134 1,77451-962

25.07.2001 -11.08.2003-2 5 65 1,01

601-111228.02.2002 -17.03.2004

-2 5 74 1,108751-1262

03.10.2002 -19.10.2004-2 4 11 0,791

901- 141215.05.2003 -02.06.2005

-2 4 38 0,8031051-1562

16.12.2003 -10.01.2006-2 4 50 0,815

1201-171226.07.2004 -15.08.2006

-2 4 53 0,8841351-1862

04.03.2005 -26.03.2007-2 4 57 0,973

1501-201206.10.2005 -25.10.2007

-2 4 29 0,8641651-2162

19.05.2006 -07.06.2008-2 4 11 0,836

1801-226319.12.2006 -06.10.2008

-2 5 151 2,324

Graph of Multifractal spectrum singularity width (Graph of Multifractal spectrum singularity width (ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at at

American index Dow Jones IndustrialAmerican index Dow Jones Industrial at period 07at period 07.10.19.10.199999--0707.1.111..20082008

1765-228425.09.2006 -07.11.2008

-2 5 174 1,984

There was a sharp drop in the index and 9 october 2002 DJIA reached an interim There was a sharp drop in the index and 9 october 2002 DJIA reached an interim minimum with a value of 7286,27.minimum with a value of 7286,27.

Dow Jones Industrial index of 15 september 2008, fell to 4.42 per cent to 10,917 Dow Jones Industrial index of 15 september 2008, fell to 4.42 per cent to 10,917 points - is the largest of its fall in a single day since 9 october 2002, reported France points - is the largest of its fall in a single day since 9 october 2002, reported France Presse. World stock markets experienced a sharp decline in major indexes in Presse. World stock markets experienced a sharp decline in major indexes in connection with the bankruptcy Investbank Lehman Brothers.connection with the bankruptcy Investbank Lehman Brothers.

Graph of Multifractal spectrum singularity width assessment (Δ(t)=αmax-αmin) at american index Dow Jones Industrial at period 07.10.1999-07.11.2008

Experimental results(DJI)Experimental results(DJI)

3 May, 1999, the index reached a value of 3 May, 1999, the index reached a value of 11014.70. Its maximum - mark 11722.98 - 11014.70. Its maximum - mark 11722.98 -

Dow-Jones indexDow-Jones index reached at 14 January 2000.reached at 14 January 2000.



American index Dow Jones IndustrialAmerican index Dow Jones Industrial at period 07at period 07.10.19.10.199999--0909.1.122..20082008

interval Qmin

Qmax N ∆

1-51207.10.1999 –18.10.2001

-2 6 47 0,91151-662

16.05.2000 -30.05.2002-2 6 57 0,935

301-81215.12.2000 -31.12.2002

-2 6 86 1,092451-962

25.07.2001 -11.08.2003-2 5 25 0,74

601-111228.02.2002 -17.03.2004

-2 5 31 0,821751-1262

03.10.2002 -19.10.2004-2 5 129 1,385

901- 141215.05.2003 -02.06.2005

-2 4 9 0,7261051-1562

16.12.2003 -10.01.2006-2 4 13 0,765

1201-171226.07.2004 -15.08.2006

-2 4 19 0,781351-1862

04.03.2005 -26.03.2007-2 4 19 0,792

1501-201206.10.2005 -25.10.2007

-2 4 15 0,7781651-2162

19.05.2006 -07.06.2008-2 4 5 0,772

1801-226319.12.2006 -06.10.2008

-2 5 77 1,185

Graph of Multifractal spectrum singularity width assessmentGraph of Multifractal spectrum singularity width assessment ((ΔΔ(t)=(t)=ααmaxmax--ααminmin)) at american index NASDAQ Composite at period at american index NASDAQ Composite at period

0707.10.19.10.199999--0707.1.111..20082008

1765-228425.09.2006 -07.11.2008

-2 6 207 1,067

Experimental results(NASDAQ)Experimental results(NASDAQ) Graph of Multifractal spectrum singularity width assessment (Δ(t)=αmax-αmin) at american index NASDAQ Composite at period 07.10.1999-07.11.2008

In August 2002 the first NASDAQ closes its branch in Japan, as well as In August 2002 the first NASDAQ closes its branch in Japan, as well as closing branches in Europe, and now it was turn European office, where closing branches in Europe, and now it was turn European office, where for two years, the number of companies whose shares are traded on the for two years, the number of companies whose shares are traded on the exchange fell from 60 to 38.exchange fell from 60 to 38.

After that happened result in a vast dropIn 2000, he reached even five thousandth mark, but After that happened result in a vast dropIn 2000, he reached even five thousandth mark, but after the general collapse of the market of computer and information technology is now in an after the general collapse of the market of computer and information technology is now in an area of up to two thousand points.area of up to two thousand points.

The index of technology companies The index of technology companies NASDAQ Composite reached its peak in NASDAQ Composite reached its peak in

March 2000.March 2000.



American index NASDAQ Composite at period 07American index NASDAQ Composite at period 07.10.19.10.199999--0909.1.122..20082008

Wavelet analysis and crisis predictionWavelet analysis and crisis prediction

где ,(t)– where ,(t)– function with zero mean centered

around zero with time scale and time horizon . Family of wavelet vectors is created from mother function

by displacement and scaling

,)()(),( , dtttxW

)(1

)(

tt

Time series f(t) representation as linear Time series f(t) representation as linear combinationcombination of wavelet functionsof wavelet functions

where jo – a constant, representing the highest level of resolution for which the most acute details are extracted .

),()()( ,,,

0

00tttf kj

kkj

jjkj

kj

dtttf kjkj )()( ,, 00

dtttf kjkj )()( ,,

WA crisis detectionWA crisis detection (experiment (experiment – 1– 1))

In experiment-1 of our study we usedIn experiment-1 of our study we used Daubechies wavelet functions decomposition (db-4 wavelet functions decomposition (db-4 ии db-12). db-12).

The goal was the detection of the signal, which could The goal was the detection of the signal, which could predict the sudden changes. Data on exchange rates predict the sudden changes. Data on exchange rates (USD) to the ruble were taken from the site www.rts.ru (USD) to the ruble were taken from the site www.rts.ru for the period 1.09.1995 - 12.02.1999for the period 1.09.1995 - 12.02.1999

The total number of numbered in the order several times The total number of numbered in the order several times in the interim for the period 1.09.1995 - 12.02.1999 was in the interim for the period 1.09.1995 - 12.02.1999 was 862 value.862 value.

Graph of changingGraph of changing RTS indexes at period RTS indexes at period 1.09.1995 – 12.02.19991.09.1995 – 12.02.1999

0

5

10

15

20

25

01.0

9.1

995

04.1

1.1

995

22.0

1.1

996

27.0

3.1

996

04.0

6.1

996

09.0

8.1

996

14.1

0.1

996

18.1

2.1

996

25.0

2.1

997

05.0

5.1

997

10.0

7.1

997

12.0

9.1

997

18.1

1.1

997

27.0

1.1

998

02.0

4.1

998

10.0

6.1

998

14.0

8.1

998

19.1

0.1

998

24.1

2.1

998

The division time series on the rangesThe division time series on the ranges

To achieve the goal of this time series was divided into 7 To achieve the goal of this time series was divided into 7 overlapping intervals located unevenly, so that the overlapping intervals located unevenly, so that the interval 4 (242-753) immediately preceding the time of interval 4 (242-753) immediately preceding the time of default and subsequent intervals captured the moment of default and subsequent intervals captured the moment of default. default.

Each interval consisted of 512 values: 1-512, 101-612, Each interval consisted of 512 values: 1-512, 101-612, 201-712, 242-753, 251-762, 301-812, 351-862.201-712, 242-753, 251-762, 301-812, 351-862.

Predicting the crisis with the help of wavelet analysisPredicting the crisis with the help of wavelet analysis

-6

-4

-2

0

2

4

6

8

10

12

13.02.1998 10.07.1998 07.09.1998 18.09.1998 30.11.1998 12.02.1999

Changes difference of maximum values of decomposition of Dobeshi-12 for the period 19.09.1997 -12.02.1999.

-20000

-15000

-10000

-5000

0

5000

10000

15000

20000

The difference of maximum coefficientsThe difference of maximum coefficients of of Daubechies -12-12 (17.10.1986- (17.10.1986-

31.12.1987) 31.12.1987)

Here we can see the positive peak earlier 01.10.87 and negative peak before 15.10.87.

This is more than 4 days before the «Black Monday».

Sharp line connects the two peaks. Obviously, this information can serve as a detector impending crisis.

42 days prior to the default Of the figure shows that the start of trading, the corresponding spike

in the dollar may be adopted point 742 (21.08.1998), a peak corresponds to 754 points (07.09.1998).

As we can see from the previous slide in the event of data processing by the Russian default, if we use the average of the indicator is the intervals difference, then we can find that the sharp increase occurring 18.09.1998, that is delayed by at least 11 days. At the same time schedule for the coefficients of wavelet functions shows us that the beginning of dramatic changes difference wavelet coefficients of expansions is a point 712 (10.07.1998).

We can, apparently, to predict the onset of default at least 42 days (10.07.1998 - 21.08.1998). At the same time increase the maximum value of this indicator in the starting time was 74.5 times (initial value = 0.15; following value = 11.23)

Wavelet Analysis for Crisis Wavelet Analysis for Crisis Detection ( experiment Detection ( experiment – – 2)2)

In our experiment, number 2, we used Daubechies wavelet functions decomposition (db-4).

The goal was the detecting the signal, which could predict the sudden changes in the index DJI (Dow Jones Index - Dow Jones). Data on DJI were taken from the site http://finance.yahoo.com for the period 7.10.1999 - 24.11.2008

The total number of numbered in the order several times in the interim for the period 7.10.1999 - 24.11.2008 at 2299 values.

Graph Graph DJIDJI change 7.10.1999- change 7.10.1999-88.1.111.2008.2008

7000

8000

9000

10000

11000

12000

13000

14000

15000

07.1

0.19

99

07.0

4.20

00

07.1

0.20

00

07.0

4.20

01

07.1

0.20

01

07.0

4.20

02

07.1

0.20

02

07.0

4.20

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Changing detailing factors wavelet decomposition of Changing detailing factors wavelet decomposition of db-4 suggest crossing a market for the period db-4 suggest crossing a market for the period

07.07.2005 - 24.11.200807.07.2005 - 24.11.2008

April 13, 202356

Financial market model FIMASIM

The main functional modules are: FMSWorld, which contains virtual world classes and relationships, FMSStandardRoles, which contains financial market classes, and others.

Standard classes of the system are: Trader (TFMTrader) Broker (TFMSBroker) Company (TFMCompany) Market, stock exchange (TFMSMarket) Strategy (TFMSStrategy) Plan (TFMSPlan) Order, transaction request (TFMSShareTransactionRequest) Transaction (TFMSShareTransactiont)

April 13, 202357

Virtual market program interface

April 13, 202358

The experiments were made with aim to find out at which values of parameters the market instability arises.

Experiment 1:Overall parameters: MARKET_MAKER_TRADER_COUNT = 2; RANDOM_TRADER_COUNT = 0; FUNDAMENTAL_TRADER_COUNT = 500; BROKER_COUNT = 5; MARKET_COUNT = 1; COMPANY_COUNT = 10; CLASSIFICATORS_COUNT = 31;

Companies: COMPANY_MAX_ASSETS = 50000000; // 50Mbyte COMPANY_MIN_ASSETS = 1000000; // 1Mbyte

Brokers: MIN_BROKER_MARKET_ACCOUNT_MONEY =

100000; // 100k. MAX_BROKER_MARKET_ACCOUNT_MONEY =

150000; // 300k. BROKER_MONEY = 10000; // 10k.

Broker and market: MAX_COMMISION_PLANS = 3;

Market maker trader parameters: MIN_MM_TRADER_CHANGE_PERCENT = 0.1; MAX_MM_TRADER_CHANGE_PERCENT = 0.5;

Random Trader parameters: MIN_RANDOM_TRADER_PORTFOLIOS = 0; MAX_RANDOM_TRADER_PORTFOLIOS = 5; MIN_RANDOM_TRADER_MONEY = 50; MAX_RANDOM_TRADER_MONEY = 2000; MIN_RANDOM_TRADER_ACCOUNT_MONEY = 200; MAX_RANDOM_TRADER_ACCOUNT_MONEY = 1000; MIN_RANDOM_TRADER_PORTF_ITEM_PRICE = 20; MAX_RANDOM_TRADER_PORTF_ITEM_PRICE = 3000; MIN_RANDOM_TRADER_RISK_AMOUNT = 0.01; MAX_RANDOM_TRADER_RISK_AMOUNT = 0.25;

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Program realization

Real price and fundamental price

distributionsMinimum, maximum and average price

distributions

April 13, 202360

Experiment 2:Overall parameters:

MARKET_MAKER_TRADER_COUNT = 2;

RANDOM_TRADER_COUNT = 0;

FUNDAMENTAL_TRADER_COUNT = 500;

BROKER_COUNT = 20;

MARKET_COUNT = 1;

COMPANY_COUNT = 10;

CLASSIFICATORS_COUNT = 31;

Companies:

COMPANY_MAX_ASSETS = 15000; // 50Mbyte

COMPANY_MIN_ASSETS = 10000; // 1Mbyte

Brokers:

MIN_BROKER_MARKET_ACCOUNT_MONEY = 100000; // 100k.

MAX_BROKER_MARKET_ACCOUNT_MONEY = 150000; // 300k.

BROKER_MONEY = 10000; // 10k.

Broker and market:

MAX_COMMISION_PLANS = 5;

Market maker trader parameters: MIN_MM_TRADER_CHANGE_PERCENT = 0.5; MAX_MM_TRADER_CHANGE_PERCENT = 0.7;

Random Trader parameters: MIN_RANDOM_TRADER_PORTFOLIOS = 0; MAX_RANDOM_TRADER_PORTFOLIOS = 3; MIN_RANDOM_TRADER_MONEY = 10; MAX_RANDOM_TRADER_MONEY = 200000;

MIN_RANDOM_TRADER_ACCOUNT_MONEY = 200; MAX_RANDOM_TRADER_ACCOUNT_MONEY = 1000;

MIN_RANDOM_TRADER_PORTF_ITEM_PRICE = 20; MAX_RANDOM_TRADER_PORTF_ITEM_PRICE = 3000;

MIN_RANDOM_TRADER_RISK_AMOUNT = 0.01; MAX_RANDOM_TRADER_RISK_AMOUNT = 0.5;

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Price time series. Experiment 2

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Experiment 3:Overall parameters:FUNDAMENTAL_TRADER_ MARKET_MAKER_TRADER_COUNT = 2; RANDOM_TRADER_COUNT = 250;COUNT = 250;

BROKER_COUNT = 5; MARKET_COUNT = 1; COMPANY_COUNT = 10; CLASSIFICATORS_COUNT = 31;

Companies: COMPANY_MAX_ASSETS = 50000000; // 50Mbyte COMPANY_MIN_ASSETS = 1000000; // 1Mbyte Brokers:MIN_BROKER_MARKET_ACCOUNT_MONEY = 100000; // 100k. MAX_BROKER_MARKET_ACCOUNT_MONEY = 300000; // 300k. BROKER_MONEY = 10000; // 10k.

Broker and market: MAX_COMMISION_PLANS = 3;

Market maker trader parameters:

MIN_MM_TRADER_CHANGE_PERCENT = 0.1;

MAX_MM_TRADER_CHANGE_PERCENT = 0.5;

Random Trader parameters:

MIN_RANDOM_TRADER_PORTFOLIOS = 0;

MAX_RANDOM_TRADER_PORTFOLIOS = 2;

MIN_RANDOM_TRADER_MONEY = 500;

MAX_RANDOM_TRADER_MONEY = 5000;

MIN_RANDOM_TRADER_ACCOUNT_MONEY = 2000;

MAX_RANDOM_TRADER_ACCOUNT_MONEY = 7000;

MIN_RANDOM_TRADER_PORTF_ITEM_PRICE = 2000;

MAX_RANDOM_TRADER_PORTF_ITEM_PRICE = 4000;

MIN_RANDOM_TRADER_RISK_AMOUNT = 0.01;

MAX_RANDOM_TRADER_RISK_AMOUNT = 0.10;

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Price time series. Experiment 3

April 13, 202364

THANK YOU

ANY QUESTIONS?

Fundamental analysisFundamental analysis Fundamental analysis is based on an assessment of market

conditions in general and assessing the future development of a single issuer.

Fundamental analysis is a fairly laborious and a special funding agencies.

Fundamental analysis depends on the news of factors. By random and unexpected news include political and natural, as well as war.

How to conduct a fundamental analysis can be divided into four separate units, correlating with each other.

Fundamental analysis Fundamental analysis technologytechnology

The first unit - is a macroeconomic analysis of the economy as a whole.

The second unit - is an industrial analysis of a particular industry.

A third unit - a financial analysis of a particular enterprise.

A fourth unit - analyzing the qualities of investment securities issuer.

Fundamental analysis technology includes an analysis of news published in the media, and comparing them with the securities markets.

Analysis MethodAnalysis Method

Keyword extraction, characterizing the market: boost or cut, the increase / decrease.

Automatic analysis using the terminology the ontology.

Processing time series (filtering, providing trends, the seasonal components).

Using neural networks to classify the flow of news and processing time series.

•Examine what news articles relevant to the company, Yahoo uses

profiling to establish consistency between articles and companies.

•For each trend formed a temporary window to explore how art

relates to the trend.

•It is believed that there is a match, if the article appeared a few

hours before the trend.

News analysis targetNews analysis target

The intensity of the flow of news dataThe intensity of the flow of news dataThe joint processing of digital and text dataThe joint processing of digital and text data

Digital data Time series

The movement of financial instruments (price / volume)

Flow intensity:

5Mb/day, on the tool

Text data

Text flows

Various types:

News, financial reports, company brochures, government documents

Flow intensity:

20Mb/day

Idea of systemIdea of system

Past articles with newsPast articles

with news

Past data pricing

securities market

Past data pricing

securities market

Building modelBuilding model

ModelModel

New arcticles

with news

New arcticles

with news

Prediction results

Prediction results

System exit

System exit

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