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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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