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The weights on past estimates of the volatility decrease exponentially as wemove back through time.Example 10.5(Exponentially decreasing weights).The EWMA model givesσ2n-1=λσ2n-2+ (1-λ)r2n-24
MS4226 TST16/17BChapter 105
MS4226 TST16/17BChapter 10City University of Hong KongDepartment of Management SciencesMS4226 Risk Management ModelsSemester B 2016/2017Chapter 10 Summary(a) If the returns per day arei.i.d.,V ar(RT) =TV ar(R)⇒σT=√Tσ(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 KongDepartment of Management SciencesMS4226 Risk Management ModelsSemester B 2016/2017Chapter 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.