The lecture Estimation of Volatility / EWMA and GARCH by Edu Pristine is from the course Archiv - Quantitative Analysis. It contains the following chapters:
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... 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 ...
... For Quants-III (Confidential).Hence we have variance estimate for next day (n) is given by (1-n) weight to recent squared return and weight to the previous variance estimate Risk-metrics ...
... ‘t’ was also an estimate. So we can substitute for it as follows...
... volatility (Std. Dev.) estimate was 1%. Actual return on Tuesday was 4%. Therefore, volatility estimate for Wednesday is estimated upwards than Tuesday i.e. 1.378% as ...
... Wednesday was 0%. What is the variance estimate for Thursday? Solution: Variance estimate for Thursday = (1-0.94) *(0%)^2 + 0.94*(1.378%)^2 = 1.78% 2 Std. Dev. = 1.34% In very short-term like daily ...
... to be very unstable then we will apply a low decay factor (giving a lot of weight to recent observations). If we expect volatility to be constant, we would apply a high decay factor (giving a more equal weight to older observations)Sum of Weights. For Quants-III (Confidential) Sum of Weights one special ...
... variance, which weight will be applied to the return that is 4 days ...
... (1-0.95) 3 *0.95 = 0.00012 for r when t = 4. B. Correct. The EWMA RiskMetrics model is defined as: ht = ?*h t-1+ (1- ?)* r 2 t-1. For t = 4, and processing r0 through the equation three times produces a factor of (1-0.95)*0.95^3 = 0.043 for r0 when t = 4. C. Incorrect. The 0.95 has not been squared. The EW ...
... that variance tends to show mean – reversion i.e. it gets pulled to a long-term Volatility rate over time. For Quants-III (Confidential) a long-term Volatility rate over ...
... sum of all the weights is equal to 1 we ge t the following equation as ...
... y estimate for next day (t+1) and long-term average volatility (to which the model shows revers ion over-time)...
... weight given to latest variance estimate (persistence factor). Therefore, 1-0.12-0.85 = 3% is weight given to long-term avera ge Volatility. Therefore, 3%*V L= 0.000005 i.e. V L= 0.017% Also, variance estimate for 0.03 + 0.02r 2 t-1 + 0.95h t-1 t= 0.02 + 0.01r 2 t-1 + 0.97h t-1 = 0.03 + 0.96 = 0.99. -B. Correct. The model that will take the shortest time to rever t to its mean is the model with the lowest persistence defined by. In this case the persistence factor is the second lowest C. Incorrect. The model that will take in the market variable is 1%. Wha t is the new variance rate? ...