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Nonlinear stock market model including
Citation preview
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