期权期货与其他衍生产品第九版课后习题与答案Chapter-（二十二）.pdf

CHAPTER 22 Value at Risk Practice Questions Problem 22.1. Consider a position consisting of a $100,000 investment in asset A and a $100,000 investment in asset B. Assume that the daily volatilities of both assets are 1% and that the coefficient of correlation between their returns is 0.3. What is the 5-day 99% VaR for the portfolio? The standard deviation of the daily change in the investment in each asset is $1,000. The variance of the portfolio’s daily change is 10002 10002 20310001000 2600000 The standard deviation of the portfolio’s daily change is the square root of this or $1,612.45. The standard deviation of the 5-day change is 161245 5 $360555 Because N-1(0.01) = 2.326 1% of a normal distribution lies more than 2.326 standard deviations below the mean. The 5-day 99 percent value at risk is therefore 2.326×3605.55 = $8388. Problem 22.2. Describe three ways of handling interest-rate-dependent instruments when the model building approach is used to calculate VaR. How would you handle interest-rate-dependent instruments when historical simulation is used to calculate VaR? The three alternative procedures mentioned in the chapter for handling interest rates when the model building approach is used to calculate VaR involve (a) the use of the duration model, (b) the use of cash flow mapping, and (c) the use of principal components analysis. When historical simulation is used we need to assume that the change in the zero-coupon yield curve between Day m and Day m 1 is the same as that between Day i and Day i 1 for different values of i . In the case of a LIBOR, the zero curve is usually calculated from deposit rates, Eurodollar futures quotes, and swap rates. We can assume that the percentage change in each of these between Day m and Day m 1 is the sam