Sample Paper

Financial Engineering (Prof. Mahendra Mehta)

End Term Exam (2 Hours – Feb 3, 2011)

Open Notes, Closed Internet, Hard-Copy exam

Question 1 – Given the following bid/offer rates (2 marks)

ü USD/JPY – 82.34/38

ü USD/INR – 45.20/25

ü GBP/USD – 1.5620/25

Find the following cross rates – USD/GBP, INR/JPY, GBP/JPY, GBP/INR (Calculate up to 2 places of decimal for currency pairs involving JPY and up to 4 decimal places for other currency pairs)

Question 2 - USD/CHF spot rate is given as 0.9600/05. The 6 month USD interest rate is 1% and 6 month CHF interest rate is 1.5% per annum. The 6 month interest rate for USD/CHF is quoted to be 0.9705/0.9708 (1+2=3 Marks). Is the quoted rate appropriate? If yes, prove that by calculation. If no, can you arbitrage? If yes, what transactions would you carry out to arbitrage?

Question 3 – Given the following, find the INR interest rate for 3 months? (2 Marks)

ü USD/INR – Spot – 45.50

ü USD/INR – 3 Month Forward rate – 46.50

ü 3 Month USD interest rate is 1%

Question 4 – Answer the following with respect to an Interest Rate Swap (1+1+2=5 Marks)

ü What is the initial value of a single currency Interest Rate Swap?

ü If you are receiving fixed & paying floating, and the yield curve is going up, what will happen to the value of the swap?

ü What is the difference between a PAR value annual coupon paying and yearly swap rate?

Question 5 – Answer the following with respect to an option (2+2=4 Marks)

ü Define Put-Call parity. What does put call parity convey?

ü If the Put-Call parity equation is violated by the market place, how can you exploit the mispricing?

Question 6 – Explain carefully the difference between hedging, speculation & arbitrage (3 Marks)

Question 7 – What is the difference between entering into a long forward contract when the forward is $50 and taking long positions in a call option with a strike price of $50? (3 Marks)

Question 8 – Explain carefully the difference between selling a call option and buying a put option (3 Marks)

Question 9 – An investor enters into a sheet forward contract to sell 100,00 GBP for US dollar at an Exchange rate of 1.5000 USD per GBP. How much does the investor gain or lose if the exchange at the end of the contract is (1) 1.4900 and (2) 1.5200? (2+2=4 Marks)

Question 10 – Suppose that you write a put contract with a strike price of $40 and an expiration date in 3 months. The current stock price is $41 and the contract is on 100 shares. What have you committed yourself to? How much could you gain or lose? (1+2=3 Marks)

Question 11 – Suppose that you own 5,000 shares worth $25 each. How can put option be used to provide you with insurance against a decline in the value of your holding over the next 4 months? (2 Marks)

Question 12 – Suppose a June put option to sell a share for $60 costs $4 and is held until June. Under what circumstances will the seller of the option (i.e., the party with the short position) make a profit? Under what circumstances will the option are exercised? Draw a diagram illustrating how the profit from a short position in the option depends on the stock price at maturity of the option. (1+1+2=4 Marks)

Question 13 – The current price of a stock is $94, and 3-month European call option with a strike price of $95 currently sells for $4.70. An investor who feels that the price of the stock will increase is trying to decide between buying 100 shares and buying 2,000 call options (=20 Contracts). Both strategies involve an investment of $9,400. What advice would you give? How high does the stock price have to rise for the option strategy to be more profitable? (2+1=3 Marks)

Question 14 – A financial institution has entered into an interest rate swap with company X. Under the terms of the swap, it receives 10% per annum and pays 6-month LIBOR on a principle of $10 million for 5 years. Payments are made every 6 months. Suppose that company X defaults on the 6^th payment date -(at the end of the year 3) when the interest rate (with semi-annual compounding) is 8% per annum for all maturities. What is the loss to the financial institution? Assume that 6-month LIBOR was 9% per annum halfway through years. (2 Marks)

Question 15 – What does it mean to assert that the delta of a call option is 0.7? How can a short position in 1,000 options be made delta neutral when the delta of each option is 0.7? (1+1=2 Marks)