The simulation of news and insiders'

influence on stock-market prices

dynamics in non-linear model

Victor Romanov, Oksana Naletova, Eugenia Pantileeva, Alexander Federyakov

Plekhanov Russian Academy of Economics

Computational Finance 2006

27 – 29 June 2006

London, UK

There exist two kinds of traders’ strategies

F- trader strategy: N-trader strategy:

The aggregate excess demand:

33 )()( ttttFt xvxvcef

ttt hvv 1

ttttNt yxyxcen )(

ttttt enwefwe )1(

tgR

tt

tt

eww

ww

)1(

1

11)1(

ttt yxy

1 11 1

/][/][t

ktj

t

ktj

jjjt

t

ktj

t

ktj

jjjtt kenxenxkefxefxR

Dynamic prices’ adjustment:

Share of the two types of investors :

ttttttt enwbefbwbexx )1(1

R - the past relative return

Common view of program interface with graphic representation of

artificial time series generated by the program and simulating

dollar/ruble exchange

The interface permits to make the substitution parameter values into the model:

alfa, Cf, Cn, w1, g, b, k, Insiders share, q, S, Noise, Strength, u, h, v1, Count, bad/good

slide and to overview the variables values.

The real

head

and

shoulder

pattern

Non-linear oscillation The strange attractor

This output looks like head and shoulder pattern

0

0,5

t

vj+1 := vj +( h * (Exp Qj - 1) / (Exp Qj + 1)) + εj

The price fundamental value is falling down

with “bad” news

The price fundamental value is rising up

with “good” news

0)(,))1/()1(*(

0)(),1)(/()1)((*))))/(((*(

**)1(

/)(

0_,

0_,

)(*

{

{

1

1 1

1

2

1

tttttt

tttttttt

t

ttttt

t

ktj

t

ktj

jjjjt

ttt

tt

t

ttt

RinsRifExpQExpQhv

RinsRifQExpQExpRinsRRinssExphvvins

einslenlwefwe

keinsxeinsxRins

RifRinsR

RifRinsRR

xxqeins

The total return including

insiders

The insiders’ return

The insiders’ past relative

return

The combined news and insiders’ influence on the price fundamental value

Excess demand now

Insiders impact on the assets market price

Insiders past relative return

Insiders’ super profit implying

market collapse

Market prices behavior in proximity of

crash point

22.5

23

23.5

24

24.5

25

25.5

26

26.5

0 20 40 60 80 100 120 140 160 180 200

Ряд1

Insiders’ return

Real data USD/ruble change rate

data during Russian default for

period 05.03.1999 – 01.11.1999

Prices’ behavior with insiders

0

2

4

6

8

10

12

14

16

18

0 100 200 300 400 500 600

Ряд1

Insiders impact on the assets market

price

Insiders past relative return

For comparison Yukos

actions open prices for

period from 13.10.2003

to 26.11.2004

Output neurons

Input neurons I

N

P

U

T

D

A

T

A

x(1)+1) x(4)+ x(6)+x(5)+ x(N)+x(3)+x(2)+

x(2) x(4)x(3)x(1)

x(5) x(7)x(6)x(4)

x(4) x(6)x(5)x(3)

x(3) x(5)x(4)x(2)

………………………………

x(N-1) x(N)x(N-1)x(N-2)

Kohonen Net input data window sliding along time series

The time series is cut into pieces to

arrange sliding data window

27

27.5

28

28.5

29

29.5

30

30.5

31

0 100 200 300 400 500 600

33.5

34

34.5

35

35.5

36

36.5

37

37.5

38

38.5

0 100 200 300 400 500 600

-0,3

-0,2

-0,1

0

0,1

0,2

0,3

0,4

0 5 10 15 20 25 30 35

Chart pattern class A Chart pattern class B

The arrows indicate places where Kohonen Net recognize patterns of classes A and B

Fractal pattern of time series discovered by Kohonen Network

-0,15

-0,1

-0,05

0

0,05

0,1

0,15

0,2

0 5 10 15

342

256

107

-0,8

-0,6

-0,4

-0,2

0

0,2

0,4

0,6

0 10 20 30 40

447

229

490

147

cyclic

stability

bearish

bullish

Classes:

Plot of Means for Each Cluster

Cluster 1

Cluster 2

Cluster 3

Cluster 4

Cluster 5

Cluster 6

Cluster 7

Var3

Var6

Var9

NewVar2

NewVar5

NewVar8

NewVar11

NewVar14

NewVar17

NewVar20

Variables

-5

0

5

10

15

20

25

30

35

Plot of Means for Each Cluster

Cluster 1

Cluster 2

Cluster 3

Var3

Var6

Var9

NewVar2

NewVar5

NewVar8

NewVar11

NewVar14

NewVar17

NewVar20

Variables

-5

0

5

10

15

20

25

30

35

0

5

10

15

20

25

30

0 100 200 300 400 500 600

Ряд1

0

4

8

12

16

20

24

0 10 20 30 40

Ряд1

-3

1

5

9

13

17

21

25

0 4 8 12 16 20 24

Ряд1

0

4

8

12

16

20

24

0 10 20 30 40

Ряд1

The number of clusters estimation by k-means method (3 clusters)

The clusters patterns discovered by Kohonen Network

USD changing rate during the period

01.08.1997-01.11.1999

6 rub/Usd 16 rub/Usd 23 rub/Usd