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1st SEMESTER 2020/21 FINAL EXAMINATION

BACHELOR DEGREE – Year 4

MTH305

RISK MANAGEMENT

Part One: Online Test Questions (45 marks)

Please attempt the following questions on the learning mall via online quiz function. Provide answers

online. No any other submission of your paper work or process for this part.

O1	Suppose that the parameters in a *GARCH(1,1)* model** are = 0.03, = 0.95 and o = 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 days?	5 marks
O2	The probability that the lossfrom a portfolio will be greater than $10 million in one month is estimated to be 5%. What is the one-month 99% VaR (in million) assuming that the power law Kx- applies with α= 3?	5 marks
O3	Suppose that the price of Asset X at close of trading yesterday was $300 and its volatility was estimated as 1.3% per day. The price of X at the close of trading today is $298. Update the volatility of X using (a) The EWMA model with 入= 0.94 (b) The GARCH(1,1) model with o = 0.000002, = 0.04, and = 0.94.	5 marks
O4	Consider a *portfolio* of *options* on a single asset. Suppose that the delta of the portfolio is 12, the value of the asset is $10, and the daily volatility of the asset is 2%. Estimate the one-day 95% VaRfor the portfoliofrom the delta.	5 marks
O5	A company has a position in *bonds* worth $6 million. The *modified* *duration* of the portfolio is 5.2 years. Assume that only parallel shifts in the yield curve can take place and that the standard deviation of the daily yield change (when yield is measured in percent) is 0.09. Use the duration model to estimate the 20-day 90% VaRfor the portfolio.	5 marks
O6	Suppose that *the* *spread* between the yield on a three-year riskless zero-coupon bond and a three-year zero-coupon bond issued by a bank is 210 basis points. The Black-Scholes–Merton price of an option is $4.10. How much should you be prepared to payfor it if you buy itfrom a bank?	5 marks
O7	Suppose that there is a 1% probability that *operational* *risk* losses of a certain type exceed $10 million. Use the power law y = Kx−a to estimate the 99.97% worst-case operational risk loss when the parameter α equals 0.25.	5 marks

Suppose that a trader has bought some illiquid shares. In particular, the trader has 100 shares of A, which is bid $50 and offer $60, and 200 shares of B, which is bid $25 offer $35.