# MAF308 Derivative and Fixed Income Securities: Financial Statement

### Questions:

The following table gives the price of bonds:

 Bond Principal (\$) Time To Maturity (Months) Annual Coupon Rate (%) Bond Price (\$) 100 6 0.0 96 100 12 0.0 90 100 18 8.0 95

Half the stated coupon is assumed to be paid every six months. Use semi-annual compounding as interest rate measurement.Calculate (annualized) zero rates for maturities of 6 months, 12 months and 18 months.

What is the fair price of 18-months zero-coupon bond given current term structure of zero rates? The par value of bond is assumed to be \$100.

Assume you are treasury manager in a company and the company requires \$1,000,000 (\$1 Million) in 6 months for the duration of 1 year. You can finance this need by trading zero-coupon bonds, i.e., buying or selling zero-coupon bonds or go to bank to organize a forward contract.

The bank quotes a forward rate 14% per annum semi-annual compounding applied from 6 months to 18 months. The prices of zero-coupon bonds with maturity 6 months and 12 months are listed in the above table and the price of zero-coupon bond with maturity 18 months is calculated in Part II.

Ignoring all the other costs and given all the information above, are you going to accept the bank’s offer? Justify your decision.

Assume you have observed the following information for a commodity:

 Spot price for commodity \$150 Forward price for expiring in 1 year \$162 Interest rate for 1 year 5% p.a. semi-annual compounding Storage cost \$1.5 p.a. payable semi-annually in arrears

Part I.

Explain why it is important to differentiate investment assets and consumption assets in regards to forward price determination.Given the above information, if you identify an arbitrage opportunity, present your strategy to take it. If you believe there might not be an arbitrage opportunity, explain why.

Assume instead you observe the following information:

 Spot price for commodity \$150 Forward price for expiring in 1 year \$155 Interest rate for 1 year 5% p.a. semi-annual compounding Storage cost \$1.5 p.a. payable semi-annually in arrears

Given the above information, if you identify an arbitrage opportunity, present your strategy to take it. If you believe there might not be an arbitrage opportunity, explain why.A trader sells a strangle by selling a call option with a strike price of \$52 for \$1 and selling a put option with a strike price of \$43 for \$8. For what range of prices of the underlying asset does the trader make a profit?

Assume that you observe the following. The spot exchange rate between the Swiss Franc and U.S. dollar was 1.0404 (\$ per franc). Interest rates in the U.S. and Switzerland were 2.5% and 1.0% per annum, respectively, with continuous compounding. The three-month forward exchange rate was 1.0503 (\$ per franc). Present a possible arbitrage strategy and show your profit.

A hedge fund is currently engaged in a plain vanilla interest rate swap with a company. Under the terms of the swap, the hedge fund receives six-month LIBOR and pays 6% per annum on a principle of \$100 million for five years. Payments are made every 6 months.  Assume that the interest rates start to soar after two years and the company defaults on the sixth payment date when the LIBOR rate is 8 percent for all maturities (with semi-annual compounding). The 6-months LIBOR rate 6-months ago is 7.5%. What is the loss to the hedge fund?

A stock price is currently \$48. Over each of the next two three-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 3% per annum with semi-annual compounding.Use the two-steps binomial tree model to price a 6-months European put option with an exercise price of \$51.Assume you have sold the above put option to your client and charged him a fair price. Discuss how you can hedge your risk to avoid a big loss if the stock price turned out to be \$1 in 6-months.Suppose you subscribe to a service that gives you estimates of the theoretically correct volatility of stocks. You note that the implied volatility of a particular option is substantially higher than the theoretical volatility. What action should you take and why?

Explain how to use call options and put options to create a synthetic short position in stock.Consider two investors who agree on the stock’s price and volatility but who do not agree on the stock’s expected return. One believes that the stock price will earn 15 percent over the next year, while the second believes that it will have a negative 5 percent return. Will they agree or disagree on the value of a one-year call option on the stock when using the Black-Scholes-Merton Model? Justify your answer. [Please note, by answering only “agree” or “disagree” without reasoning, a zero mark will be awarded.]