Insiders modeling london-2006
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The document summarizes a simulation of news and insider influences on stock market price dynamics using a non-linear model. It describes two types of trader strategies (F and N), how aggregate excess demand is calculated, dynamic price adjustment, and how the share of each trader type changes over time based on past relative returns. It also discusses using the model to simulate dollar/ruble exchange rates and analyze patterns in the time series data.
![There exist two kinds of traders’ strategies
F- trader strategy: N-trader strategy:
ef t cF (vt xt )3 (vt xt )3 ent cN ( xt yt ) xt yt
vt vt 1 h t yt xt 1 (1 ) yt 1
The aggregate excess demand:
et wt ef t (1 wt )ent
Dynamic prices’ adjustment:
xt 1 xt bet bwt ef t b(1 wt )ent
wt
Share of the two types of investors : wt 1
wt (1 wt )e gRt
t 1 t 1 t 1 t 1
R - the past relative return Rt [ xt ef
j t k
j x ef
j t k
j j ] / k [ xt en
j t k
j x en ] / k
j t k
j j](https://image.slidesharecdn.com/insidersmodeling-london-2006-110415052540-phpapp01/85/Insiders-modeling-london-2006-2-320.jpg)
Insiders modeling london-2006
- 1. 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
- 2. There exist two kinds of traders’ strategies F- trader strategy: N-trader strategy: ef t cF (vt xt )3 (vt xt )3 ent cN ( xt yt ) xt yt vt vt 1 h t yt xt 1 (1 ) yt 1 The aggregate excess demand: et wt ef t (1 wt )ent Dynamic prices’ adjustment: xt 1 xt bet bwt ef t b(1 wt )ent wt Share of the two types of investors : wt 1 wt (1 wt )e gRt t 1 t 1 t 1 t 1 R - the past relative return Rt [ xt ef j t k j x ef j t k j j ] / k [ xt en j t k j x en ] / k j t k j j
- 3. 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.
- 4. Non-linear oscillation The strange attractor The real head and shoulder pattern This output looks like head and shoulder pattern
- 5. 0,5 0 t
- 6. vj+1 := vj +( h * (Exp Qj - 1) / (Exp Qj + 1)) + εj The price fundamental value is rising up The price fundamental value is falling down with “good” news with “bad” news
- 7. eins t q * ( xt xt 1 ) 2 The insiders’ return The total return including R Rins t , if _ R 0 insiders Rt 1 { t Rt Rins t , if _ Rt 0 The insiders’ past relative t 1 t 1 return Rins t ( x j eins j t k j x eins j t k j j )/k et wt ef t (1 w l ) * ent l * eins t Excess demand now The combined news and insiders’ influence on the price fundamental value vt (h * Exp ( s ( Rins t /( Rt Rins t )))) * ( Exp (Qt ) 1) /( Exp (Qt ) 1), if ( Rt Rins t ) 0 vinst 1 { vt (h * ( ExpQt 1) /( ExpQt 1)) t , if ( Rt Rins t ) 0
- 8. Insiders impact on the assets market price Insiders’ super profit implying market collapse Insiders past relative return Market prices behavior in proximity of crash point
- 9. 26.5 26 25.5 25 24.5 Ряд1 24 23.5 23 22.5 0 20 40 60 80 100 120 140 160 180 200 Prices’ behavior with insiders Real data USD/ruble change rate data during Russian default for period 05.03.1999 – 01.11.1999 Insiders’ return
- 10. 18 16 14 12 10 Ряд1 8 6 4 2 0 0 100 200 300 400 500 600 Insiders impact on the assets market price For comparison Yukos actions open prices for period from 13.10.2003 to 26.11.2004 Insiders past relative return
- 11. I Input neurons N Output neurons P U T D A T A
- 12. x(1)+1) x(2)+ x(3)+ x(4)+ x(5)+ x(6)+ x(N)+ x(1) x(2) x(3) x(4) x(2) x(3) x(4) x(5) x(3) x(4) x(5) x(6) x(4) x(5) x(6) x(7) Kohonen Net input data window sliding along time series ……………………………… x(N-1) x(N-2) x(N-1) x(N) The time series is cut into pieces to arrange sliding data window
- 14. 0,4 0,3 0,2 0,1 0 0 5 10 15 20 25 30 35 -0,1 -0,2 -0,3 Chart pattern class A Chart pattern class B 31 38.5 38 30.5 37.5 30 37 29.5 36.5 29 36 35.5 28.5 35 28 34.5 27.5 34 27 33.5 0 100 200 300 400 500 600 0 100 200 300 400 500 600 The arrows indicate places where Kohonen Net recognize patterns of classes A and B
- 15. Fractal pattern of time series discovered by Kohonen Network Classes: cyclic 0,2 0,15 0,1 342 stability 0,05 256 0 107 0 5 10 15 -0,05 -0,1 -0,15 bearish 0,6 0,4 0,2 447 bullish 0 229 0 10 20 30 40 -0,2 490 147 -0,4 -0,6 -0,8
- 16. Plot of Means for Each Cluster Plot of Means for Each Cluster 30 35 35 30 30 25 25 25 20 20 20 15 15 15 Ряд1 10 10 10 5 5 Cluster 1 0 Cluster 2 0 5 Cluster 3 Cluster 4 -5 Cluster 5 -5 Var3 Var9 NewVar5 NewVar11 NewVar17 Cluster 1 Cluster 6 Var3 Var9 NewVar5 NewVar11 NewVar17 0 Var6 NewVar2 NewVar8 NewVar14 NewVar20 Var6 NewVar2 NewVar8 NewVar14 NewVar20 Cluster 2 Cluster 7 Cluster 3 0 100 200 300 400 500 600 Variables Variables USD changing rate during the period 01.08.1997-01.11.1999 The number of clusters estimation by k-means method (3 clusters) 25 24 24 21 20 20 17 16 16 13 12 Ряд1 Ряд1 12 Ряд1 9 8 8 5 4 4 1 0 0 0 10 20 30 40 -3 0 4 8 12 16 20 24 0 10 20 30 40 6 rub/Usd 16 rub/Usd 23 rub/Usd The clusters patterns discovered by Kohonen Network