Some questions (in the attached file) about swaps, options and portfolio insurance

QUESTION 1 (3 + 2 + 2 + 3 + 1 + 1 = 12 marks) Two international clients Qantas and General Motors are interested in changing the nature of their liabilities. Based on their credit ratings they have been offered the following rates which are compounded annually on a $100 million (AUD) six-year loan: Company Qantas General Motors AUD (six-year rates) 7% 6.50% USD (six-month rates) LIBOR + 2% LIBOR + 1% At the time of the contract initiation, 1 USD is worth AUD 1.34. Qantas requires an American dollar loan and General Motors requires an Australian dollar loan. Design a cross-currencyinterest-swap that will net us (the bank) acting as an intermediary 10 basis points (0.10%) per annum. Also, design the swap so that it will be equally attractive to both companies and: a) Will eliminate foreign exchange risk for both companies. b) Allow Qantas to minimize foreign exchange risk by 1% and allow General Motors to reduce foreign exchange risk by 0.5%. c) Is the interest rate that General Motors is paying via the cross-currency-interest-swap fixed? If General Motors floating-rate spread above LIBOR increases from (LIBOR + 1%) to (LIBOR + 1.5%) is this an additional cost from General Motors perspective (explain your answer with reference to the swap that you designed in part (a))? d) Assume that under the terms of a cross-currency-interest-swap which is between Qantas and General Motors and arranged by us (the bank) the following: the notional principal is $100,000,000 (AUD) for six years, and the exchange rate is 1 USD is equal to 1.34 AUD at the time the contract was initiated. We the bank require a fee of 0.10% per annum. Qantas has agreed to pay 6-month LIBOR+1.95% per annum (annual compounding) in USD and to receive 3.9% per annum (annual compounding) in AUD with semi-annual payments. Assume that the swap has 19 months remaining until maturity and the exchange rate at this time is that 1 USD is worth AUD 1.355. Assume that the AUD interest rate is 2.22% per annum and the USD interest rate is 1.55% per annum with continuous compounding for all maturities. The 6-month LIBOR rate five months ago was 2.95% per annum. Calculate the value of the swap to Qantas (i.e., in AUD)? e) Discuss the exposure to us (the bank) to market risk in the cross-currency-interest-swap described in part (d)? f) Discuss the exposure of us (the bank) to credit risk in the cross-currency-interest-swap described in part (d) if General Motors was to default on their side of the swap AND that we (the bank) are unable to find a replacement for General Motors in the cross-currencyinterest-swap? QUESTION 2 (2 + 3 + 3 + 3 + 1 + 2 = 14 marks) The consensus across different investment banks suggests that there will be low volatility in the technology sector over the next four month period. APPLE a technology stock was trading at $98.66 but due to a recent stock split is currently trading at $34.94. Jaslyn Chen, Joel Hawkins, Hannah and Rachael Murray, and Tom Zhang are new clients of the bank and who have previously only ever traded APPLE stocks before. (a) From your knowledge of derivative securities prepare a brief which you will pitch to your new clients to explain the uses and benefits from utilizing the derivative market. Keep your brief to a maximum of half-an-A4 page. You may refer to a recent working paper which can be downloaded from: http://papers.ssrn.com/sol3/papers.cfm? abstract_id=2480870. Mr Zhang says that a friend of his (Daniel Michaels) mentioned that he has generated trading profits in the past using: (b) a butterfly spread using call options, (c) a strangle using in-the-money options, (d) a straddle. Using the four-month European APPLE stock options from the following list, construct the tables and the diagrams showing the profit-loss (as a function of the terminal stock price) of each component position as well as of the combined position of these strategies to show Mr Zhang how he could profit from these strategies. Provide separate graphs for the butterfly spread, strangle and straddle. Option type Strike price Option Premium Call $30 $6.57 Call $35 $2.45 Call $40 $0.84 Put $30 $0.22 Put $35 $1.94 Put $40 $5.24 (e) Discuss and compare the performance of each strategy with respect to the set up cost and the profit/loss potential. What is your recommendation to Mr Zhang? (f) Mr Hawkins heard the phrase \"implied volatility\" from a friend of his (Chris Matthews). Use Excel's GoalSeek Tool function to complete the table and estimate implied volatility (correct to 4 decimal places). Assume the risk-free rate is 3% per annum and the dividend yield is 1.5% per annum both with continuous compounding. Call prices Call IV Put prices Put IV K = $30 K = $35 K = $40 $5.10 $1.50 $0.25 $0.17 $1.67 $5.19 QUESTION 3 [8 + 2 + 2 + 2 = 14 marks] As a valued member of the UTS alumni, you have been asked to be a guest lecturer for Lecture 8 and 9 for Derivative Securities (25620). Vinay has asked you to go through calculating option prices using the binomial tree and Black-Scholes model. Through Bloomberg you identify the following characteristics of the USD/AUD currency pair: 1 USD = 1.34 AUD US risk-free rate = 0.75% per annum with continuous compounding Australian risk-free rate = 1.75% per annum with continuous compounding Volatility of the USD/AUD exchange rate is 40% per annum. Given your expertise in currency options you decide to use a four-step binomial tree to calculate the following option prices (to four decimal places): (a) A European two-year call option to buy 1 USD for 0.75 AUD. In addition, calculate the value of the same option using the Black-Scholes model. Compare and comment. (b) An American two-year call option to buy 1 USD for 0.75 AUD. (c) A two-year up-and-out barrier call option with a strike of 0.75 AUD and knockout barrier of 2.50 AUD. An up-and-out call option gives the holder the right to buy the underlying asset at the strike price on the expiration date. When the price of the underlying asset is above the barrier, the option is "knocked-out" and does not carry any value for such nodes of the tree. (d) Vinay has asked you to spend 30 minutes discussing specifically the role of mortgage backed securities in causing the global financial crisis. Please provide a summary of your lecture. Your summary must be brief and a maximum of one A4 page. QUESTION 4 [3 + 3 + 2 + 2 = 10 marks] The S&P 500 index is currently at 2560 and the dividend yield of the index is 1.85% per annum with simple compounding. The risk-free interest rate is 2.30% per annum with simple compounding and the volatility of the index is 33% per annum. (a) A family of high net worth clients (Lily, James and Alex Price) each have a well-diversified stock portfolio worth $150 million. The portfolio has a beta of 0.85 and the dividend yield on the portfolio is 2.10% per annum with simple compounding. The high net worth clients are worried about the direction of the market and have requested your help to protect the value of their portolio. Describe the options portolio insurance strategy that they should each apply to prevent the portfolio from falling below $125 million in four months. Available index options are quoted in increments of five index points. (b) What is the cost of this portfolio strategy for each member of the Price family? For simplicity, please assume that the dividend yield on the index is 1.85% per annum and the risk-free rate is 2.3% per annum, and that both of these interest rates are continuously compounded. (c) If the level of the market in four months is 2850 index points, calculate the gain or loss of the strategy and discuss the outcome of the insurance strategy. (d) If the level of the market in four months crashes to 700 index points, calculate the gain or loss of the strategy and discuss the outcome of the insurance strategy