Learning Objectives: Apply the GARCH (1,1) model to estimate volatility. Explain and apply approaches to estimate long horizon volatility/VaR and describe the process of mean reversion according to a GARCH (1,1) model. Evaluate implied volatility as a predictor of future volatility and its shortcomings. Describe an example of updating correlation estimates
24.6.1. Within Bank XYZ, the risk reporting and analysis is conducted by a central group. They utilize the EWMA approach, building up the volatility history with over four years of data (over 1,000 observations for each variable). Their selection of lambda is 0.93.
It was discovered that there was an error in the data input for the return on equity A1 four trading days ago. Whereas the return was originally reported as -1.50% it was actually 15.00%.
The previous forecast volatility is 4.00%. After making the correction, which of the following ranges would the updated volatility fall into?
a. Between 4.01% and 4.50%
b. Between 4.51% and 5.00%
c. Between 5.01% and 5.50%
d. Between 5.51% and 6.00%
24.6.2 Jeremy is looking through his colleagues’ GARCH model that estimates the volatility of oil trading prices over time. He notices that the model is not correct and that Alpha is too high. What would happen to the model when alpha is adjusted in the updated model?
Original Model = γ = 11%, α = 0.070, β = 0.820, ω = 0.001859
Updated Model = γ = 13%, α = 0.050, β = 0.820, ω = 0.002197
a. Volatility will revert quicker to σ²(LR) which is approximately 0.0169.
b. Volatility will revert quicker to σ²(LR) which is approximately 0.13.
c. Volatility will revert slower to σ²(LR) which is approximately 0.13.
d. Volatility will revert slower to σ²(LR) which is approximately 0.0169.
24.6.3 A large international bank uses EWMA for its risk system, with a decay factor of 0.92. On day T, the current correlation forecast is 15.0%. If on day T respectively, which of the following is closest to the new correlation?
a. 12.5%
b. 13.4%
c. 15.0%
d. 16.2%
Answers here:
24.6.1. Within Bank XYZ, the risk reporting and analysis is conducted by a central group. They utilize the EWMA approach, building up the volatility history with over four years of data (over 1,000 observations for each variable). Their selection of lambda is 0.93.
It was discovered that there was an error in the data input for the return on equity A1 four trading days ago. Whereas the return was originally reported as -1.50% it was actually 15.00%.
The previous forecast volatility is 4.00%. After making the correction, which of the following ranges would the updated volatility fall into?
a. Between 4.01% and 4.50%
b. Between 4.51% and 5.00%
c. Between 5.01% and 5.50%
d. Between 5.51% and 6.00%
24.6.2 Jeremy is looking through his colleagues’ GARCH model that estimates the volatility of oil trading prices over time. He notices that the model is not correct and that Alpha is too high. What would happen to the model when alpha is adjusted in the updated model?
Original Model = γ = 11%, α = 0.070, β = 0.820, ω = 0.001859
Updated Model = γ = 13%, α = 0.050, β = 0.820, ω = 0.002197
a. Volatility will revert quicker to σ²(LR) which is approximately 0.0169.
b. Volatility will revert quicker to σ²(LR) which is approximately 0.13.
c. Volatility will revert slower to σ²(LR) which is approximately 0.13.
d. Volatility will revert slower to σ²(LR) which is approximately 0.0169.
24.6.3 A large international bank uses EWMA for its risk system, with a decay factor of 0.92. On day T, the current correlation forecast is 15.0%. If on day T respectively, which of the following is closest to the new correlation?
a. 12.5%
b. 13.4%
c. 15.0%
d. 16.2%
Answers here:
