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  • Why Stock Markets Crash
  • Why stock markets crash?
    • Sornette’s argument in his book/article is as follows:
    • The motion of stock markets are not entirely random in the ’normal’ sense.
    • Crashes in particular are ’abnormal’ and have a certain statistical signature.
    • A plausible model of trader behaviour during crashes is based on ’copying’ or ’herd mentality’.
    • The statistical signature produced by such models is close to that seen in the markets.
    • Fitting parameters of copying models to stock market data gives a reasonable fit.
    • Sornette and his colleagues have predicted the occurance of particular crashes.
  • Mathematics applied to social sciences
    • Sornette’s argument in his book is as follows:
    • The motion of stock markets are not entirely random in the ’normal’ sense (observation) .
    • Crashes in particular are ’abnormal’ and have a certain statistical signature (observation/statistics) .
    • A plausible model of trader behaviour during crashes is based on ’copying’ or ’herd mentality’ (model) .
    • The statistical signature produced by such models is close to that seen in the markets (solution) .
    • Fitting parameters of copying models to stock market data gives a reasonable fit (data fitting) .
    • Sornette and his colleagues have predicted the occurance of particular crashes (prediction) .
  • Mathematics applied to social sciences
    • Sornette’s argument in his book is as follows:
    • The motion of stock markets are not entirely random in the ’normal’ sense (observation) .
    • Crashes in particular are ’abnormal’ and have a certain statistical signature (observation/statistics) .
    • A plausible model of trader behaviour during crashes is based on ’copying’ or ’herd mentality’ (model) .
    • The statistical signature produced by such models is close to that seen in the markets (solution) .
    • Fitting parameters of copying models to stock market data gives a reasonable fit (data fitting) .
    • Sornette and his colleagues have predicted the occurance of particular crashes (prediction) .
  • Course Outline
    • Short, Medium and Long Term Fluctuations
    • Pricing Derivatives (Johan Tysk)
    • Positive feedbacks, negative feedbacks and herd behaviour.
    • Networks and phase transitions. (Andreas Grönlund)
    • Log-periodicity and predicting crashes.
    • Stock Market Crash Day.
  • The Dow Jones 1790-2000
  • The Dow Jones 1980-1987
  • Short, Medium & Long Term Fluctuations in Returns
    • Returns are usually defined as (p(t+dt)-p(t))/p(t) .
  • Short term fluctations
  • Autocorrelation
  • Trading strategy
    • Can use correlation with past to predict the expected future.
    • Profit is determined by standard deviation of return fluctuations (say approx 0.03%).
    • Invest $10,000, 20 trades a day, 250 days a year: 10000*(1.0003) 5000 =$44,806 (!).
    • But transaction cost must be less than $3 per $10,000.
  • Medium term fluctations
  • Medium term fluctations
  • Efficient market hypothesis
    • (Samuelson 1965)
  •  
  • Example: .
  • Efficient market hypothesis
    • Axiom of expected price formation based on rational, all-knowing agents.
    • Noise generated by underlying noise in the value of the world (similar variance).
    • Any irrational, ill-informed agents will generate more noise, but will over time be pushed out the market by rational agents.
    • Relies on agents not using Y t in their pricing of futures (no copying each other).
  • Long time scale patterns
  • Hidden patterns?
    • Autocorrelation does not detect all patterns.
  • Hidden patterns?
    • Autocorrelation does not detect all patterns.
    • Look at drawdowns instead.
  • Drawdown distribution
  • Drawdown distribution
  • Largest drawdowns
  • Constructing a confidence interval
    • Take all days of time series and reshuffle them.
    • Find the distribution of resulting drawdowns.
  • Confidence interval
  • Stretched exponential model
  • Power laws (Mantegna & Stanley, 1995)
  • Power laws (Mantegna & Stanley, 1995)
  • Summary
    • Costs too high to gain from short term correlations.
    • Medium term fluctations are usually exponentially distributed.
    • In the long term there are occasional drawdowns (crashes) which are inconsistent with the exponential model.
    • Other apparent structures in the market.