# 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?