Shane Whelan University College Dublin

1
Phynance Pioneering Approaches by Physicists to
Model Markets

• Shane Whelan University College Dublin
• Shane.Whelan_at_ucd.ie

2
Is Financial Economics ? Economics?

• Social scientists for the most part dont seem
  to have learned that the theory is always
  required to fit the data, and that it is an
  incorrect procedure that data should be made fit
  the theoryAs a class social scientists have
  never caught on to this. As a result they very
  often wont even undertake an investigation and
  collect data unless they have some sort of a
  theory or model to fit the data to.
• Osborne, M.F.M. (1977), The Stock Market and
  Finance from a Physicists Viewpoint, p. 19.

3
Alternative History of Financial Economics
Emergence of Phynance as a separate discipline
1991
Fischer Black Myron Scholes The Pricing of
Option Contracts and Corporate
Liabilities. Robert Merton Theory of Rational
Option Pricing.
1973
Work of Probabilists Levy, Cramér, Wiener, Kolmog
orov, Doblin, Khinchine, Feller, Itô.
1963
Benoit Mandelbrot The Variation of certain
Speculative Prices
1959
M.F.M Osborne Brownian Motion in the Stock Market
1953
Maurice Kendall The Analysis of Time Series,
Part I Prices.
1944
John von Neumann Oskar Morgenstern Theory of
Games and Economic Behaviour.
Alastair Murray The Compilation of Index Numbers
and Yield Statistics relative to Stock Exchange
Securities Charles Douglas Statistical Groundwork
for Investment Policy.
1930
1929
1900
Louis Bachelier Theory of Speculation.
4
Phynance as distinct discipline

• 1991 finance papers start being published in
  leading physics journals,
• Levy walks and enhanced diffusion in Milan Stock
  Exchange, Mantegna, Physica A, 179, 232-242.
• Momentum from mid-1990s
• 1997 Eugene Stanley coined term econophysics
• Clusters of excellence
• Stanley, Mantegna, et al
• Tails of distributions, Levy flights, percolation
• Sornette et al
• Self-organised criticality, ruptures,
  log-periodic oscillations
• Solomon et al
• Agent models
• The Prediction Company (formerly Doyne Farmer)
• Olsen Group (Müller, Pictet, Dacorogna)
• Science Finance (Bouchard, Potters)

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Physics -v- Economics

• Theories in Physics account for known phenomena
  and make predictions which can be confronted with
  data
• Arguments in Physics can be resolved with further
  data
• Data does not play such a central role in
  economics or traditional finance as approached by
  economists - EMH, CAPM, APT.
• Conclude, financial economics enriched by
  differing approach of physicists

6
Actuaries better in tune with Physicists Approach?

• It is a capital mistake to theorize before one
  has data. Insensibly one begins to twist facts to
  suit theories, instead of theories to suit
  facts.
• Sherlock Holmes (or A. Conan Doyle) , A Scandal
  in Bohemia.

7
Preface to Open our Minds

• Returns series are non-stationary.
• Seasonality in mean, e.g., time-of-the day,
  day-of-the-week, month-of-the-year, semi-annual
  effects.
• But all statistical evidence still regarded as
  contentious with hypothesis dismissed as
  data-mined.
• Temporal change in (unconditional) covariance
  structure of returns.
• Key Reference Loretan Phillips Testing the
  covariance stationary of heavy-tailed time
  series. Journal of Empirical Finance, 1, 211-248
  (1994).
• Conclusion I Past returns are not a guide to
  future returns (at least not in any
  straightforward way) is true statistically.
• Conclusion II All stationary models of returns
  do not capture essence of return series (so, in
  particular, excludes all ARIMA and ARCH models).

8
See for Ourselves

• There is nothing like first-hand evidence.
• Sherlock Holmes, A Study in Scarlet

9
Annual Log-Return, Irish Equity Market, 1783 -
1998
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Monthly Log-Return Irish Equity Market, Jan. 1934
- Aug. 1998
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Daily Log-Returns, Irish Equity MarketDec.
1987-Aug 1998
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Evolution of Returns on Irish Market Compared to
UK US, 1934-2000
13
Returns on Irish Market Independent of Other
Markets
Irish v- UK market, 1934-69
Irish v- US market, 1934-69
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In Search of Empirical Regularities (or Stylized
Facts)

• It is of the highest importance in the art of
  detection to be able to recognise out of a number
  of facts which are incidental and which vital.
  Otherwise your energy and attention must be
  dissipated instead of being concentrated.
• Sherlock Holmes, The Reigate Puzzle
• It has long been an axiom of mine that the little
  things are infinitely the most important.
• A Case of Identity

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Time Domain Analysis

• Primitive is log-returns
• Key tool of analysis (time domain)
• Generalised to

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Stylized Fact - 1

• Low autocorrelations in return series
• at high frequency, close to zero for most liquid
  markets when time-scale is greater then about 15
  minutes
• at lower frequency (weekly, monthly), a small
  positive autocorrelation (but not exploitable due
  to market frictions)

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Stylized Fact - 2

• Heavy-tailed distributions
• Similar shape irrespective of ?t

18
QQ Plot Monthly Returns on Daily
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QQ Plot Annual Returns on Daily
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Stylized Fact - 2

• Heavy-tailed distributions
• Similar shape irrespective of ?t
• Not in domain of attraction of stable distribution

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Limiting Distributions of IID Sums
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Histogram of Filtered (Daily) ISEQ Return-General
Log-Returns Against Best Fitting Symmetric Stable
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Using Hill Estimator

• Gives Point Estimates of
• 2.8 for daily data (both tail)
• 2.3 for monthly (both tails)
• 2.8 (right tail) and 1.6 (left tail)
• Unreliable point estimator - significant bias.
• Asymptotic properties not well-understood when
  data not iid.

24
Other Studies

• Loretan Phillips (1994) Testing the covariance
  stationarity of heavy-tailed time series. Journal
  of Empirical Finance, 1, 211-248.
• Exchange rates Stock indices have tail indices
  in range, 2.4-3.8
• Müller, U.A., Dacorogna, M.M., Olsen, R.B.,
  Pictet, O.V. (1998) Heavy Tails in High-Frequency
  Financial Data. In A Practical Guide to Heavy
  Tails Statistical Techniques and Application.
  Editors Adler, R.J., Feldman, R.E. Taqqu,
  M.S., Birkhäuser, US.
• Stanley et al. (1999), Scaling of the
  distribution of price fluctuations of individual
  companies Phys. Rev E60, 6519-6529
• For timescales, 5 min to 16 days, tail index of
  shares is about 3 (2.8 using Hill).
• Stanley et al. (1999), Scaling of the
  distribution of fluctuations of financial market
  indices Phys. Rev E60, 5305-5316

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Stylized Fact - 2

• Heavy-tailed distributions
• Similar shape irrespective of ?t
• Not in domain of attraction of stable
  distribution
• So thick that 4th moment is unlikely to exist

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Stylized Fact - 2

• Heavy-tailed distributions
• Similar shape irrespective of ?t
• Not in domain of attraction of stable
  distribution
• So thick that 4th moment is unlikely to exist
• still evident when volatility clustering removed
  (by ARCH models, etc) but now less heavy

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Stylized Fact - 3

• Volatility Clustering
• Positive correlation of volatility measures with
  time
• Power-law decay with increasing time distance,
  i.e.,

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Stylized Fact - Others

• 4 Intermittency
• on any time-scale, returns exhibit irregular
  bursts in volatility (heavy-tailed conditional
  distribution)
• 5 Volume-Volatility Correlation high
• 6 Others...
• - asymmetry between large positive and negative
  movement (latter more frequent)
• leverage effect, where the correlation of the
  return to future (instantaneous) volatility is
  negative decaying to zero.

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Stylized Facts

• The more bizarre a thing is the less mysterious
  it proves to be. It is your commonplace,
  featureless crimes which are really puzzling,
  just as a commonplace face is the most difficult
  to identify.
• Sherlock Holmes, The Red Headed League

30
Guessing the DGP

• Kinetic Theory of Gases develops explanation of
  macro thermal phenomena from micro mechanical
  structure
• Gives big surprise in that the laws governing the
  micro interactions are time reversible but they
  lead to time irreversibility on the macro-scale
• Here agents in market trying to outwit each other
  - and leading to identical patterns
• irrespective of market (so dealing structures
  irrelevant)
• irrespective of time-scale (so institutional
  structures of market players irrelevant)
• So can simple stylized agent model replicate the
  stylized facts?

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Guessing the DGP

• Keynes beauty contest revisited with Arthurs El
  Faro problem and minority games to simulate
  learning from limited information (a basic
  feedback mechanism into prices)
• patterns in the strategies effectively employed
  ensure no equilibrium is reached, i.e., prices
  will fluctuate even without new information
• More realistic agent models (replicating many
  stylized facts) are reporting...
• if markets reach what looks looks an equilibrium
  then there remain exploitable patterns
• trend followers induce trends but with an
  oscillatory feature, which favours different
  trend following rules (!)
• not all value strategies push market values
  closer to fundamental value (!)

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Flights of Fancy

• Physicists a bit like Chicken Licken (according
  to Osborne).
• Sornette finds parallel with stock market crashes
  and ruptures in metals
• before a crash, superexponential growth in prices
  evident
• underlying growth curve decorated with
  log-periodic oscillations making them more easily
  detectable
• some predictive success already
• now claims a singularity in stock market series,
  world GDP and world population in 2050,
  (preceded by a singularity in computer power in
  2030).

Source Sornette, D. (2003), Why Stock Markets
Crash Critical Events in Complex Financial
Systems, PUP.
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Lets not get carried away...Modelling Orders
of Complexity

• Level 1 - Two body problem
• e.g., gravity, light through prism, etc.
• Level 2 - N-identical body with local interaction
• e.g., Maxwell-Boltzmanns thermodynamics
• Ising model of ferromagnetism
• Level 3 - N-identical body with long-range
  interaction
• Level 4 - N-non-identical body with
  multi-interactions
• Modelling Markets
• Modelling economics systems generally

From Roehner, B.M., Patterns of Speculation A
Study in Observational Econophysics, CUP 2002
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Physicists Approach to Finance Phynance

• We approached the case, you remember, with an
  absolutely blank mind, which is always an
  advantage. We had formed no theories. We were
  simply there to observe and to draw inferences
  from our observations.
• Sherlock Holmes, The Adventure of the Cardboard
  Box.

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Selected Websites

• Best Econophysics Source Site (Papers, data,
  books, conferences, links, etc)
• http//www.unifr.ch/econophysics/
• Websites of Couple of Leading Researchers
• Didier Sornette
• http//www.ess.ucla.edu/faculty/sornette/
• Doyne Farmer
• http//www.santafe.edu/jdf/
• Websites of Companies applying methods
• Olsen Associates
• http//www.olsen.ch/
• Science Finance
• http//www.science-finance.fr/