The weights on past estimates of the volatility decrease exponentially as we

# The weights on past estimates of the volatility

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The weights on past estimates of the volatility decrease exponentially as we move back through time. Example 10.5 (Exponentially decreasing weights) . The EWMA model gives σ 2 n - 1 = λσ 2 n - 2 + (1 - λ ) r 2 n - 2 4 MS4226 TST16/17B Chapter 10 5 MS4226 TST16/17B Chapter 10 City University of Hong Kong Department of Management Sciences MS4226 Risk Management Models Semester B 2016/2017 Chapter 10 Summary (a) If the returns per day arei.i.d.,V ar(RT) =TV ar(R)σT=(b) The law asserts thatP(V > x) =Kx-α(c) The estimate for the volatility per day is the sample standard deviation ofreturnsˆσ=sr,wheres2r=1n-1nsummationdisplayi=1(ri-¯r)2.(d) The EWMA model isσ2n=λσ2n-1+ (1-λ)r2n-1. 6 City University of Hong Kong Department of Management Sciences MS4226 Risk Management Models Semester B 2016/2017 Chapter 10 Question1. The volatility of independent and identically distributed returns of an asset is2% per day. What is the standard deviation of the return in three days?2. The volatility of an asset is 25% per annum. Suppose that daily returns areindependent and identically distributed.(a) What is the standard deviation of the return in one trading day?(b) Assume that the daily returns have a normal distribution with zero mean.Find the 95% confidence limits for the return in one day.3. Why do traders assume 252 rather than 365 days in a year when using volatil-ities?4. The number of visitors to websites follows the power law such thatP(V > x) =Kx-2.Suppose that 1% of sites get 500 or more visitors per day.  • • • 