Modeling financial markets- cellular automata thinking Financial - - PDF document

▶
modeling financial markets cellular automata thinking
SMART_READER_LITE
LIVE PREVIEW

Modeling financial markets- cellular automata thinking Financial - - PDF document

Jun 23, 2023 772 likes •1k views

Modeling financial markets- cellular automata thinking Financial markets foundations Agent-based computational finance heterogeneous agents agents interacting locally : Cont-Bouchaud model (modeling an emerging market)

slide-1
SLIDE 1

1

Modeling financial markets- cellular automata thinking

  • Financial markets foundations
  • Agent-based computational finance

– heterogeneous agents – agents interacting locally :

  • Cont-Bouchaud model

(modeling an emerging market)

  • cellular automata models of local

interaction

slide-2
SLIDE 2

2 Financial markets foundations:

Efficient Market Hypothesis (Fama, Samulsen) Three pilars:

information

MARKET

price

slide-3
SLIDE 3

3

Stock markets

95 96 97 98 99 00 01 02 03 04 05 06

DJ, FTSE, DAX

2000 4000 6000 8000 10000 12000 14000

WIG values

5000 10000 15000 20000 25000 30000 DJ Industrial London FT-SE DAX WIG

If Agents are rational Market is efficient Then Price is represented by a random walk Financial markets foundations:

Efficient Market Hypothesis (Fama, Samulsen)

Capital Asset Pricing Model ( Sharpe, Lintner)

Three pilars:

slide-4
SLIDE 4

4

Agents have homogeneous expectations:

stocks bonds

All investors hold the same portfolio:

Financial markets foundations:

Efficient Market Hypothesis (Fama, Samulsen) Capital Asset Pricing Model ( Sharpe, Lintner)

Black-Scholes option pricing formula ( +Merton)

Three pilars:

slide-5
SLIDE 5

5 Financial markets foundations:

Efficient Market Hypothesis (Fama, Samulsen) Capital Asset Pricing Model ( Sharpe, Lintner) Black-Scholes option pricing formula ( +Merton) Three pilars:

q q

1000 1200 1400 1600 1800 2000 2200 2400 2600 2800 3000 WIG Electrim zywiec

  • Return( t, time-horizon ) = log Price( t+ time-horizon ) – log Price( t )
  • Volatility ( t , time-horizon ) = | Return( t , time-horizon ) |
  • Volume (t )
slide-6
SLIDE 6

6

W IG

  • 4
  • 2

2 4 1 1 1 1

too many too little too many

  • 3

1 ) | (| x x return P ∝ >

!" ##$

% & &

  • & '

( )*(+#,

slide-7
SLIDE 7

7 Complex system modeling

  • a population of different elements with well defined microscopic attributes

and interacting.

  • show emergent macroscopic phenomena:
  • self-organization ( functional-organization )
  • unpredictability
  • evolution through punctuated equilibriums ( step-wise response )

Independent Agents models:

' " "

slide-8
SLIDE 8

8 Independent Agents models:

Strong simplifications: agents share the same information agents act independently

  • .)

" * , * , Independent Agents models:

Strong simplifications: agents share the same information agents act independently

  • .)

" * , * ,

  • Bak, Paczuski, Shubik ( 97 )
  • Gardina, Bouchaud ( 2002)
slide-9
SLIDE 9

9 Bak, Paczuski, Shubik ( 97 )

Sell(4,t)

Sell(3,t)

Buy(6,t)

Sell(2,t)

Buy(1,t) Buy(7,t) Buy(5,t) Sell(8,t)

B1 B2 B3 B4 B7 B8 B5 B6

  • Gardina, Bouchaud ( 2002)
slide-10
SLIDE 10

10 B1 B2 B3 B4 B7 B8 B5 B6

  • Gardina, Bouchaud ( 2002)

Agents interacting locally

  • & / -" "

R.Cont and J.P.Bouchaud, Macroeconomic Dynamics (2000)

slide-11
SLIDE 11

11 B1 B2 B3 B4 B7 B8 B5 B6 B1 B2 B3 B4 B7 B8 B5 B6

∆ P(t)= Σ demand(i) –Σ supply(i)

slide-12
SLIDE 12

12

p Percolation Probability 1 pc

L=200

cluster size

100 101 102 103 104

frequency in 20000 experiments

100 101 102 103 104 105 106 107 108 109 power-law with 1.77 exponent p=0.1 p=0.2 p=0.3 p=0.4 p=0.5 p=0.6 p=0.7 p=0.8 p=0.9

log log

slide-13
SLIDE 13

13 CA approach to Count- Bouchaud model

D.Stauffer and T.J.P.Penna (1998)

Large investor

Small investor

pc=0.592746….. CA approach to Count- Bouchaud model

Large investor

Small investor

D.Stauffer and T.J.P.Penna (1998)

∆ P(t)= Σ demand(i) –Σ supply(i)

pc=0.592746

slide-14
SLIDE 14

14

  • Daily

returns distribution

DFA exponents

10 20 30 40 50 60 70 0.20 0.25 0.30 0.35 0.40 0.45 0.50 0.55 0.60 first 10 days exponents after a month exponents

D.Makowiec, Acta Phys. Pol B (2004)

  • KGHM Polska Miedz

date 1998 1999 2000 2001 2002 2003 2004 Volume 100 101 102 103 104 105 106 107 price 10 20 30 40 volume price histogram of daily returns normalized daily returns

  • 4
  • 2

2 4 probability 0.001 0.01 0.1 BPH Bank Przemyslowo-Handlowy 1998 1999 2000 2001 2002 2003 2004 Volume 100 101 102 103 104 105 106 107 price 150 200 250 300 350 volume price histogram of daily returns normalized daily returns

  • 4
  • 2

2 4 probability 0.001 0.01 0.1

slide-15
SLIDE 15

15 A1 A2 B1 B2 B3 B4 B7 B8 B5 B6 1223.&)23

  • )""

" A3

  • price

price

  • a=0.1

normalized returns

  • 2
  • 1

1 2

probability

0.001 0.01 0.1 b=0.0 b=0.1 b=0.2 b=0.3 b=0.4 b=0.5

4#+56 5###+

slide-16
SLIDE 16

16 A1 A2 B1 B2 B3 B4 B7 B8 B5 B6

"

D.Makowiec, P.Gnacinski and W.Miklaszewski, Physica A331 (2004) 269

  • "
  • 5

"

Assumption: Information is available to some agents

  • nly

A1 A2 B1 B2 B3 B4 B7 B8 B5 B6

"

"

slide-17
SLIDE 17

17 A1 A2 B1 B2 B3 B4 B7 B8 B5 B6

  • "-

"

slide-18
SLIDE 18

18 4###+ 4###+

slide-19
SLIDE 19

19 4###+ 4###+

slide-20
SLIDE 20

20 Examples of CA models: q Lattice gas dynamics persistency

Stauffer, Oliveira and Bernardes(1999)

q Evolving network tail decay with exponent 2.5

Equiluz&Zimmermann (2000)

q Spin ferromagnetic interaction- tail decay with exponent 4

Chowdhury, Stauffer(1999), Bornholdt (2001)

q Forest fire rule – multifractal properties

Bartolozzi& Thomas (2004)

q Local trend rule – less locality then more stable market

Bandini, Manzoni,Naimzada& Pave (2 004)

slide-21
SLIDE 21

21