EWMA and GARCH Model
About the Lecture
The lecture EWMA and GARCH Model by Edu Pristine is from the course Archiv - Valuation and Risk Models. It contains the following chapters:
- EWMA Model
- EWMA - Question - Example 1
- EWMA - Question - Example 2
- EQMA Weights Graph
- How to select a Decay Factor
- Question: FRM Exam
- GARCH (1,1)
- GARCH - Question
- Question: FRM Exam
- Question 2
Author of lecture EWMA and GARCH Model
Edu Pristine
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Excerpts from the accompanying material
... this equation, variance for time ‘t’ was also an estimate.So we can substitute for it as follows: EduPristine For VaR-I (Confidential)2 What are the weights for old returns and variance is called ...
... Tuesday was 1%. Find volatility estimate for Wednesday using ...
... Std. Dev. = sqrt (1.9%) = 1.378% Tuesday volatility (Std. Dev.) estimate was 1%. Act ual return on Tuesday was ...
... actual return on Wednesday was 0%. What is the variance ...
... Dev. = 1.34% In very short term like daily returns, estimated vo latility is the expected return Since latest return of 0% ...
... VaR-I (Confidential)7 Weight of variance termsDays into the ...
... 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 app ly a high decay factor (giving a more equal weight to older observations)Sum of Weights One special property of the weights used in the EWM A formula is that their sum will ...
... variance, which weight will be appl ied to the return that is 4 days ...
... of (1-0.95) 3 0.95 = 0.00012 for 0 when t = 4. B. Correct. The EWMA RiskMetrics model is defined as: h t= 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 0 when t = 4. C. Incorrect. The 0.95 has not been squared. ...
... recognizes that variance tends to show mean – reversion i.e. it gets pulled to a long-term Volatility rate over time. EduPristine For VaR (Confidential)0 a long-term Volatility rate ...
... 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) ...
... the weight given to latest variance estimate (persistence factor). Therefore, 1-0.12-0.85 = 3% is weight given to long-term average Volati lity. Therefore, 3%*V L= 0.000005 i.e. V L= 0.017% Also, variance estimate ...
... + 0.02r 2 t-1 + 0.95h t-1 C.h t= 0.02 + 0.01r 2 t-1 + 0.97h t-1 D.ht= ...
...= 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 1 +. In this case the persistence factor is the second lowest: 1 + ? = 0.02 + 0.95 = 0.97. C. Incorrect. The model that will take ...
... in the market variable is 1%. Wha t is the new variance rate? ...
... we can substitute for it as follows. For VaR-I (Confidential) 34. What are the weights for old returns and variance? λ is ...
... Tuesday was 1%. Find volatility estimate for Wednesday using λ ...
... Dev. = sqrt (1.9%) = 1.378% Tuesday volatility (Std. Dev.) estimate was 1%. Actual return on Tuesday was 4%. ...
... actual return on Wednesday was 0%. What is the variance estimate ...
... = 1.34% In very short-term like daily returns, estimated volatility is the expected return. Since latest return of 0% was ...
... (Confidential) 39. Weight of variance terms. Days into the ...
... 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: One special property of the weights used in the EWMA formula is that their sum will always equal ...
... weight will be applied to the return that is 4 days old. ...
... The EWMA RiskMetrics model is defined as: h t= λ*h t-1+ (1- λ)* 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 r 0 when t = 4. C. Incorrect. The 0.95 has not been squared. The EWMA RiskMetrics model is ...
... recognizes that variance tends to show mean-reversion i.e. it gets pulled to a long-term volatility rate over time. For VaR-I (Confidential) 43 a long-term volatility rate ...
... sum of all the weights is equal to 1 we get the following equation as well: ...
... 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 average volatility. Therefore, 3%*V L= 0.000005 i.e. V L= 0.017%. Also, variance estimate for ...
... B. Correct. The model that will take the shortest time to revert to its mean is the model with the lowest persistence defined by α1 + β. In this case the persistence factor is the second lowest: α1 + β = 0.02 + 0.95 = 0.97. C. Incorrect. The model that will ...
... is 1%. What is the new variance rate? ...
... approach is the delta-normal VAR. Non-Parametric Approach: - Historical Simulation, -Multivariate Density Estimation ...
... the realized returns from (t-1) to t. For the most recent k returns: Choose lamda based on weight requirements (L). For VaR-I (Confidential) 52: Assign a weight ...
... Disadvantage: Correlations tend to increase in periods of stress. This approach might underestimate the portfolio Volatility Extend ...
