End term Exam

Risk Management

Final Exam (Open Book, Open Laptop)

Feb 4, 2010 (Prof: AV Vedpuriswar)

Marks: 50

1) A swap involves an outflow of $ 1.5 million and an inflow of Pound 1 million every 3 months. If the dollar interest rate is 3% per annum, the Pound interest rate is 5% per annum and the current exchange rate is $1.4 / Pound, find the present value of the swap. Assume stable interest and exchange rates. Also assume the maturity of the swap is 1 year. (5 Marks)

2) Calculate the implied volatility of a call option trading at Rs 5 if the underlying stock price is Rs 40, the risk free rate of interest is 8% and the strike price is Rs 45. If the historical volatility of the stock is 20% per annum, what kind of arbitraging possibilities do you envisage? Assume the maturity of the option is 1 year. (8 Marks)

3) A portfolio of options written on the stock has a delta of 250. How can you make it delta neutral? Will delta neutrality eliminate all the risk or will any risks remain? (4 Marks)

4) If 1 day VaR is $5 million and there is an auto-correlation of 0.3 between daily returns, what is the 3 day VaR? (5 Marks)

5) A company has a market value of $5 billion with a volatility of 20% per annum. The liabilities are in the form of a single zero coupon bond redemmable 3 years from now at $4 billion. The risk free rate of interest is 4% per annum. Calculate the cumulative probability of default and the value of equity (8 Marks)

6) A Credit default swap has a maturity of 2 years. A default can take place only during the middle of the year. The marginal risk neutral probability of a default in a year is 2%. In case of default, the amount recoverable is 50% of the face value of the bond. If the risk free rate of interest is 8% per annum, what is the spread payable at the end of each year? (9 Marks)

7) A risk free bond and a risky bond both are maturing in 3 years and paying a coupon of 6% payable annually. The risk free bond is yielding 4% while the risky bond yielding 5%. Estimate the expected loss due to credit risk. Assume both bonds will be redemmed at the face value of $ 1,000,000 at maturity (6 Marks)

8) The daily losses on a portfolio for the past 30 days are (in $ million) 1,2,1,2,3,4,5,3,2,1,4,6,2,1,7,1,3,2,3,4,3,1,5,6,2,1,3,2,7,8. What is the cut-off point for the 90% 10 day VaR? (5 Marks)