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Estimation of Volatility

  • Let xi be the continuously compounded return during day i (between the end of day “i-1” and end of day “I”)
  • Let σn be the volatility of the return on day n as estimated at the end of day n-1
  • Variance estimate for next day is usually calculated as:
    • Variance = average squared deviation from average return over last ‘n’ days

  • Mean of returns (x-bar) is usually zero, especially if returns are over short-time period (say, daily returns). In that case, variance estimate for next day is nothing but simple average (equally weighted average) of previous ‘n’ days’ squared returns.


  • What if the volatility is dependent on the values of volatility observed in the recent past?
  • What if they also depend on the latest returns?


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