PERCOLATION MODEL OF FINANCIAL MARKET

Transcription

1 PERCOLATION MODEL OF FINANCIAL MARKET Byachkova Anastasiya Perm State National Research University Simonov Artem KPMG Moscow

2 Econophysics - using physical models in financial analysis Physics and economy are both based: on the theory of random walks on the collective behavior of large numbers of correlated variables

3 Sources Bouchaud J.-P. An introduction to statistical finance// Physica A, 313, C Chang I., Stauffer D., Pandey R.B. Asymmetries, correlations and fat tails in percolation market model// International Journal of Theoretical and Applied Finance, Vol.5, No. 6, C Stauffer D. Percolation models of financial market dynamics// Advances in Complex Systems, Vol.4, No.1, C Stauffer D., Sornette D. Self-organized percolation model for stock market fluctuation// Physica A, 271, C Sornette D., Stauffer D., Takayasu H. Market Fluctuation II: multiplicative and percolation models, size effects and prediction// arxiv:cond-math/ , Vo1. 30, Gould H., Tobochnik J. An Introduction to Computer Simulation Methods Applications to Physical Systems, Part 2

4 2 L a p buy n s p c () t Parameters of model - quantity of traders in the market; - probability of traders activity; - probability of traders decision to buy - count of cluster, which includes s traders; - probability of percolation threshold appearance; - price change for one iteration

5 Parameters of model a -measure of time interval to which one iteration corresponds Cluster of traders Is active with probability 2a sleep with probability 1 2a a ; 10 2

6 Parameters of model Trader buy with probability Sell with probability p buy p sell 1 p buy Cluster of traders buy 2ap buy sell 2ap sell sleep 1 2a

7 Parameters of model price change = different between demand and supply () t n s n s s s buy sell n s distribution of near the percolation threshold follows the scaling low n s f [( p p ) s ] s c

8 Appearance of percolation threshold = market crash (we have an infinite cluster in our lattice) p - average strength and number of interaction when p p c The main part of traders have the same opinion

9 pc Monte Carlo simulation of percolation model К iterations Generate lattice: every lattice has random number [0, 1] Find the percolation threshold p c Choose р lattices are occupied or empty with probability p Find the value pc Form clusters Find the value Checking the percolation threshold Analyze results p c

10 p 0,5 Example

11 Influence of parameters Empirical distributions of Δ with different value of p buy 1,2 1 0,8 0,6 0,4 delta (p buy=0.6) delta (p buy=0.9) delta (p buy=0.1) delta (p buy=0.5) 0,2 0 Empirical distributions of Δ with different value of a 1,2 1 0,8 0,6 0,4 delta (a=0.01) delta (a=0.1) delta (a=0.499) 0,2 0

12 Model calibration

13 Algorithm of model calibration Processing market data The sample of real price changes for some time period Optimization part Monte Carlo simulation of percolation model The sample of model price changes Calculation of the distance between the model and the actual distribution of price changes

14 Calculation of the distance between the model and the actual distribution of price changes Kullback-Leibler divergence: Base on information theory Non-symmetric Always nonnegative Possible to use in case, when you don t know the form of distribution (nonparametric)

15 Optimization algorithm

16 Optimization algorithm Realization in R DEoptim global optimization algorithm class of genetic algorithms, which use biology-inspired operations possible to use for discontinuous and nondifferentiable functions

17 Results Вид функций распределения модельных и фактических значений 1,2 1 0,8 0,6 Функция распределения фактических данных Функция распределения модельных данных 0,4 0,2 0

18 Conclusions Empirical function of percolation threshold and price change for one iteration Creating real market model Possibility of model development

19 Thank you for your attention!

20 p 0,8 Example

21 Results 60 pс frequency histogram Average 0,594 Mode 0,595 Median 0,583 SD 0,03 Kurtosis 0,11 Asymmetry 0,186 Empirical function of pс distribution 1 0,9 0,8 0,7 0,6 0,5 0,4 0,3 0,2 0,1 0 0,520,530,540,550,560,570,580,590,600,610,620,630,640,650,660,670,680,690,700,710,72

22 percolation threshold p ( N) lim p ( N) c N N quantity of traders in the market c P c dependence from agents quantity 0,61 0,6 0,59 0, , , , ,58 0,57 0,56 0,55 0,54 0,53 0, , , Quantity pc 0,5991 0,3731* 1,131 N

23 Another ways of calculation of the distance between the model and the actual distribution of price changes Fisher information metric Jensen Shannon divergence