1 / 58

Why on earth are physicists working in ‘economics’? Trinity Finance Workshop September 26 2000

Summary Introduction A brief look at some data, stylised facts Rationale for interest of physicists Agent models Minority game and simulations Lotka Volterra Peer pressure models Crashes. Why on earth are physicists working in ‘economics’? Trinity Finance Workshop September 26 2000.

cana
Télécharger la présentation

Why on earth are physicists working in ‘economics’? Trinity Finance Workshop September 26 2000

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Summary Introduction A brief look at some data, stylised facts Rationale for interest of physicists Agent models Minority game and simulations Lotka Volterra Peer pressure models Crashes Why on earth are physicists working in ‘economics’?Trinity Finance Workshop September 26 2000 Peter Richmond Department of Physics Trinity College Dublin

  2. Systems

  3. Fluctuations: S(t, ) = ln[P(t+ )/P(t)] Price P(t) Time t

  4. ~15% pa ~8% pa

  5. FT All share index 1800-2001

  6. Ln FTA: 1800-1950;1950-2001

  7. Dow Jones 1896-2001

  8. Z,R,S • If P(t+Δ)~P(t) or Δ« t then S(t) = Ln[P(t+Δ)/ P(t)] ~R(t)

  9. Average 0.024

  10. Brownian or random walks (see TCD schools web site) Distance Time

  11. Bachelier (1900) (pre-dated Einstein’s application of Brownian motion to motion of large particles in ‘colloids’) • Theorie de la Speculation Gauthiers-Villars, Paris Gaussian tails 0

  12. Example: D1/2 = 0.178 r = 0.087

  13. FTSE100 Daily data

  14. Led to… • Efficient market hypothesis, capital asset pricing model Markowitz 1965 • Black-Scholes equation for option pricing 1973 • Nobel Prize for Economics 1992 • But did it work?

  15. …the ultimate in mega-disasters! Caveat emptor… even with Nobel Prize winners!!

  16. Overthrow of economic dogma • Martingale <xt+1>=xt • Independent, identical differences - iid • Valid only for t >> * • BUT * is comparable with timescales of importance ….where tails in pdf are important • From observation tails are NOT Gaussian • Tails are much fatter!

  17. PDF is not Gaussian Discontinuity ..(cusp in pdf)..?

  18. ‘Near’ tails and ‘far’ tails stable Levy may not even be valid for near tails

  19. Volatility persistence and anomalous decay of kurtosis • Volatility is positively correlated • Over weeks or months

  20. Anomalous decay of kurtosis

  21. Bounded Rationality and Minority Games – the ‘El Farol’ problem

  22. Agents and forces

  23. Forces in people -agents buy Hold Sell

  24. The Ising model of a magneta Prototype model of Statistical physics Focus on spin I. This sees: a)local force field from other spins b)external field, h I h

  25. Cooperative phenomenaTheory of Social Imitation Callen & Shapiro Physics Today July 1974Profiting from Chaos Tonis Vaga McGraw Hill 1994

  26. Time series and clustered volatility • T. Lux and M. Marchesi, Nature 397 1999, 498-500 • G Iori, Applications of Physics in Financial Analysis, EPS Abs, 23E • A Ponzi,

  27. Auto Correlation Functions and Probability Density

  28. Langevin Models • Tonis Vaga Profiting from Chaos McGraw Hill 1994 • J-P Bouchaud and R Cont, Langevin Approach to Stock Market Fluctuations and Crashes Euro Phys J B6 (1998) 543

  29. A Differential Equation for stock movements? • Risk Neutral,(β=0); • Liquid market, (λ-)>0) • Two relaxation times • 1 = (λ-)~ minutes • 2 = 1 / ~ year • =kλ/ (λ-)2

  30. Risk aversion induced crashes ?

  31. Speculative Bubbles

  32. R Gilbrat, Les Inegalities Economiques, Sirey, Paris 1931 O Biham, O Malcai, M Levy and S Solomon, Generic emergence of power law distributions and Levy-stable fluctuations in discrete logistic systems Phys Rev E 58 (1998) 1352 P Richmond Eur J Phys B In 2001 P Richmond and S Solomon cond-mat, Int J Phys Over-optimistic; over-pessimistic;

  33. Generalised Langevin Equations

  34. PDF fit to HIS

  35. Generalised Lotka-Volterra wealth dynamics Solomon et al • a – tax rate • a/NΣw – minimum wage • w – total wealth in economy at t • c – measure of competition

  36. GLV solution • Mean field • Relative wealth • And Ito

  37. Lower bound on poverty drives wealth distribution!

  38. Why is ~1.5? • 1+2 or 2+4 dependents • 1+3 dependents • …. • 1+9

  39. Generalised Langevin models Choose simple exponential: f(x1+x2) ~ f(x1)f(x2)

  40. Link to Marsili and Solomon (almost) Leads to Marsili within mean field approximation: P(x1,x2|t)=P(x1|t)P(x2|t) Autocatalytic term of GLV Scale time t/ζ -> t

  41. Logistic map f is analytic Discrete time & Maps

  42. Lorentz Cauchy Singular term Corresponds to autocatalytic term in GLV

  43. Levy like map

More Related