Question 8Consider again the situation in Question 7. Suppose that a secondtraded option with a delta of 0.1, a gamma of 0.5 and a vega of 0.6is available. How could the portfolio be made delta, gamma andvega neutral?Question 9 Suppose that a bank has $10 billion of 1-year loan and $30 billionof 5-year loan. These are financed by $35 billion of 1-year depositand $5 billion of 5-year deposit. The bank has equity totaling $2billion and its return on equity is currently 12%. Estimate whatchange in interest rates next year will lead to the bank's return onequity being reduced to zero. Assume that the bank is subject to atax rate of 30%.Question 10Suppose that observations on a stock price (in $) at the end ofeach of 15 consecutive days are as follows:30.2, 32.0, 31.1, 30.1, 30.2, 30.3, 30.6, 30.9, 30.5, 31.1, 31.3, 30.8, 30.3, 29.9, 29.8Estimate the daily volatility using both exact and approximateapproaches?Question 11 Suppose that the price of an asset at the close of trading yesterdaywas $300 and its volatility was estimated as 1.3% per day. The3
price at the close of trading today is $298. Update the volatilityestimate using the EWMA model with = 0.94.Question 12The probability that the loss from a portfolio will be larger than$10 million in one month is estimated to be 5%.(a) What is the VaR (1 month, 99%), assuming that the change invalue of the portfolio is normally distributed with zero mean?