Derivatives (Comm 4202) Assignment #2 - Due February 27, 2018

1.(10 marks).Suppose that the six-month rate is 5% and the nine-month rate is 6%. The rate that can be locked in for the period between six months and nine months using an FRA is 7%. What arbitrage opportunities are open to investors? All rates are continuously compounded.

2.(10 marks). The 6-month, 12-month. 18-month, and 24-month zero rates are 4%, 4.5%, 4.75%, and 5% with semiannual compounding, respectively.

(a)What is the value of an FRA that promises to pay you 6% (with semiannual payment) on a principal of $1 million for the six-month period starting in 18 months?

(b)If the six-month LIBOR rate were 6.5% with semiannual compounding in 18 months, what would be the payoff to the lender in Part (a)?

3.(10marks). An investor writes 5 naked call option contracts with a strike price of 60 and 4 naked put option contracts with a strike of 40. The underlying asset price is traded at $50 a share, the call option is priced at $3, and the put option is traded at $5. Calculate the initial margin requirement. Assume one contract is 100 shares.

4.(10marks). A trader creates a bear spread by selling a 6-month put option with a $25 strike price for $2.15 and buying a 6-month put option with a $29 strike price for $4.75. What is the initial investment? What is the total payoff when the stock price in 6 months is (a) $23, (b) $28, and (c) $33.

5.(10marks). A trader sells a strangle by selling a 6-month European call option with a strike price of $50 for $3 and selling a 6-month European put option with a strike price of $40 for $4. For what range of prices of underlying asset in 6 months will the trader make a profit? How much will the trader lose if the the price of the underlying asset is $60 in 6 months?

6.(10marks). What trading position is created from a long strangle and a short straddle when both have the same time to maturity? Assume that the strike price in the straddle is halfway between the two strike prices of the strangle. Is net trading cost always negative? Why?

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7.(10marks). It is February 27, 2018. The futures price for the June 2018 Treasury bond futures contract is 118-23.

(a)Calculate the conversion factor for a bond maturing on January 1, 2037,paying a coupon of 10%.

(b)Calculate the conversion factor for a bond maturing on October 1, 2042,paying coupon of 7%.

(c)Suppose that the quoted prices of the bonds in (a) and (b) are 169.00 and136.00, respectively. Which bond is cheaper to deliver?

(d)Assuming that the cheapest to deliver bond is actually delivered on June25, 2018, what is the cash price received on delivery of the bond?

8.(15 marks). It is February 27, 2018. The cheapest-to-deliver bond in a December 2018 Treasury bond futures contract is an 8% coupon bond with a conversion factor of 1.2195, and delivery is expected to be made on December 31, 2018. Coupons on the bond are paid on March 1 and September 1 each year. The term structure is flat, and the rate of interest with continuous compounding is 5% per annum. The current quoted bond price is $137. Calculate the quoted futures price for the contract.

9.(15marks). The December Eurodollar futures contract is quoted as 98.40 and a company plans to borrow $8 million for three months starting in December at LIBOR plus 0.5%.

(a)What rate can then company lock in by using the Eurodollar futures contract? Long or short the Eurodollar futures contract? How many contracts? (b) What position should the company take in the contracts?

(c) If the actual three-month LIBOR turns out to be 1.3% with quarterly compounding, How would explain that the company can borrow at the lock-in rate in part (a)?

Ignore timing mismatches between the cash flows from the Eurodollar futures contract and interest rate cash flows.

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