ECOM055 – Risk Management For Banking
Problem Set 8
Based on Book Chapter 10 银行风险管理代做
10.19.
Suppose that the price of an asset at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price at the close of trading today is $298.
Update the volatility estimate using
(a) The EWMA model with λ = 0.94,
(b) The GARCH(1,1) model with ω = 0.000002, α = 0.04, and β = 0.94.
10.21. 银行风险管理代做
Suppose that the parameters in a GARCH(1,1) model are α = 0.03, β = 0.95, and ω = 0.000002.
(a) What is the long-run average volatility?
(b) If the current volatility is 1.5% per day, what is your estimate of the volatility in 20, 40, and 60 days?
(c) What volatility should be used to price 20-, 40-, and 60-day options?
(d) Suppose that there is an event that increases the volatility from 1.5% per day to 2% per day. Estimate the effect on the volatility in 20, 40, and 60 days.
(e) Estimate by how much the event increases the volatilities used to price 20-, 40-, and 60-day options.
10.23.
The probability that the loss from a portfolio will be greater than $10 million in one month is estimated to be 5%.
(a) What is the one-month 99% value at risk (VaR) assuming the change in value of the portfolio is normally distributed with zero mean?
(b) What is the one-month 99% VaR assuming that the power law applies with a = 3?
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