Statistical Physics Approaches to Financial Fluctuations

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Statistical Physics Approaches to Financial
Fluctuations

• Fengzhong Wang
• Advisor H. Eugene Stanley
• Dec 13, 2007

Collaborators Philipp Weber, Woo-Sung Jung,
Irena Vodenska, Kazuko Yamasaki and Shlomo Havlin

• Scaling and Memory of Intraday Volatility
  Return Intervals in Stock Markets,
• Phys. Rev. E 73, 026117 (2006).
• Statistical Regularities in the Return
  Intervals of Volatility,
• Eur. Phys. J. B 55, 123 (2007).

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Outline

• Questions
• What are financial fluctuations?
• Why we study?
• Databases
• Results
• Scaling
• Memory
• Long-term correlations
• Take home message

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What are financial fluctuations?
Ex Stock Price and Shares Traded
Why study financial fluctuations?

• Help understand markets and control risk

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Databases Analyzed

• DAILY DATA
• U.S.A. Stocks, 1962-2007, total107 records?
• Foreign Exchange Rates, 1971-2007, total105
  records?
• Crude Oil Futures, 1985-2007, total104 records?
• INTRADAY DATA
• Trades And Quotes 2001-2002, every U.S.A.
  transactions, total109 records?
• ?30 stocks Dow Jones Industrial Average (DJIA),
  
• sampling interval1 min, total107 records
• SP 500 Index 1984-1996, total105 records,
• sampling interval10 min

?from Yahoo Finance ?from Federal Reserve ?from
Energy Information Administration ?from New York
Stock Exchange.
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How to Calculate Volatility?

• Step 1 Compute price change log(p(t1)/p(t))

Step 2 Remove intraday pattern by dividing A(s)
Step 3 Normalize by standard deviation
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Our Approach Return Intervals ?q of Volatility
Step 1 CHOOSE a threshold q
Step 2 Calculate all time intervals between
volatilities above q
?q3
?q2
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Result 1 Scaling in Return Intervals
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Result 2 Universality
B) w.r.t. Stock Names
A) w.r.t. Sampling Intervals
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How to Analyze Memory?
Divide return intervals into 8 subsets S1, S2,
, S8
S8
Stock GE
S1
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Result 3 Conditional PDF
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How to Measure Long-Term Correlation?Method
Detrended Fluctuation Analysis
d
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Result 4 Detrended Fluctuation Analysis
Surprise Return interval correlations
?Volatility correlations
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Result 5 Universality in Correlations
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Take Home Message

• Return intervals scale.
• Scaling is universal for many markets and many
  time scales.
• Return intervals show memory.
• Scaling and memory are related to long-term
  correlations in volatility.