Questions and Answers of Future of Business

A trader enters into a short forward contract on 100 million yen. The forward exchange rate is $\$ 0.0090$ per yen. How much does the trader gain or lose if the exchange rate at the end of the
On May 8, 2013, as indicated in Table 1.2, the spot offer price of Google stock is $\$ 871.37$ and the offer price of a call option with a strike price of $\$ 880$ and a maturity date of
A US company knows it will have to pay 3 million euros in three months. The current exchange rate is 1.3500 dollars per euro. Discuss how forward and options contracts can be used by the company to
The price of gold is currently $\$ 1,400$ per ounce. The forward price for delivery in 1 year is $\$ 1,500$ per ounce. An arbitrageur can borrow money at $4 \%$ per annum. What should the
Describe how foreign currency options can be used for hedging in the situation considered in Section 1.7 so that (a) ImportCo is guaranteed that its exchange rate will be less than 1.5700, and (b)
Suppose that in September 2015 a company takes a long position in a contract on May 2016 crude oil futures. It closes out its position in March 2016. The futures price (per barrel) is $\$ 88.30$
A trader buys two July futures contracts on orange juice. Each contract is for the delivery of 15,000 pounds. The current futures price is 160 cents per pound, the initial margin is $\$ 6,000$ per
Suppose that, on October 24, 2015, a company sells one April 2016 live cattle futures contract. It closes out its position on January 21, 2016. The futures price (per pound) is 121.20 cents when it
It is July 2014. A mining company has just discovered a small deposit of gold. It will take 6 months to construct the mine. The gold will then be extracted on a more or less continuous basis for 1
Trader A enters into futures contracts to buy 1 million euros for 1.3 million dollars in three months. Trader B enters in a forward contract to do the same thing. The exchange rate (dollars per euro)
One orange juice futures contract is on 15,000 pounds of frozen concentrate. Suppose that in September 2014 a company sells a March 2016 orange juice futures contract for 120 cents per pound. In
The author's website (www.rotman.utoronto.ca/ hull/data) contains daily closing prices for crude oil and gold futures contracts. You are required to download the data for crude oil and answer the
A company wishes to hedge its exposure to a new fuel whose price changes have a 0.6 correlation with gasoline futures price changes. The company will lose $\$ 1$ million for each 1 cent increase in
It is now October 2014. A company anticipates that it will purchase 1 million pounds of copper in each of February 2015, August 2015, February 2016, and August 2016. The company has decided to use
Suppose that 9 -month and 12 -month LIBOR rates are $2 \%$ and $2.3 \%$, respectively. What is the forward LIBOR rate for the period between 9 months and 12 months? What is the value of an FRA
It is January 9, 2015. The price of a Treasury bond with a $12 \%$ coupon that matures on October 12, 2030, is quoted as 102-07. What is the cash price?
It is May 5, 2014. The quoted price of a government bond with a $12 \%$ coupon that matures on July 27, 2024, is $110-17$. What is the cash price?
On June 25, 2014, the futures price for the June 2014 bond futures contract is 118-23.(a) Calculate the conversion factor for a bond maturing on January 1,2030, paying a coupon of $10 \%$(b)
How would you measure the dollar duration of a swap?
Explain what is meant by (a) the 3-month LIBOR rate and (b) the 3-month OIS rate.Which is higher? Why?
‘‘When banks become reluctant to lend to each other the 3-month LIBOR–OIS spread increases.’’ Explain this statement.
Why do derivatives traders sometimes use more than one risk-free zero curve for discounting?
Explain the collateral rate adjustment. Under what circumstances is it nonzero?
OIS rates have been estimated as 3.4% per annum for all maturities. The 3-month LIBOR rate is 3.5% per annum. For a 6-month swap where payments are exchanged every 3 months the swap rate is 3.6% per
Explain why CVA and DVA are calculated for the whole portfolio of transactions a bank has with a counterparty, not on a transaction-by-transaction basis.
Suppose that the 1-year LIBOR rate is 4% and 2-year, 3-year, and 4-year LIBOR-forfixed swap rates with annual payments are 4.2%, 4.4%, and 4.5%. All rates are annually compounded.(a) If LIBOR is used
The 1-year LIBOR zero rate is 3% per annum and the LIBOR forward rate for the 1- to 2-year period is 3.2%. The 3-year swap rate for a swap with annual payments is 3.2%. All rates are annually
Suppose the 1-year and 10-year LIBOR-for-fixed swap rates are 3% and X% (with annual payments). The 1-year and 10-year OIS swap rates are 50 basis points lower than the corresponding LIBOR-for-fixed
Assume that a non-dividend-paying stock has an expected return of $\mu$ and a volatility of $\sigma$. An innovative financial institution has just announced that it will trade a security that
Show that the formula in equation (17.12) for a put option to sell one unit of currency $A$ for currency B at strike price $K$ gives the same value as equation (17.11) for a call option to buy
Show that, if $C$ is the price of an American call with exercise price $K$ and maturity $T$ on a stock paying a dividend yield of $q$, and $P$ is the price of an American put on the same
The one-year forward price of the Mexican peso is $\$ 0.0750$ pe MXN. The US risk-free rate is $1.25 \%$ and the Mexican risk-free rate is $4.5 \%$. The exchange rate volatility is $13 \%$.
The formula for the price $c$ of a European call futures option in terms of the futures price $F_{0}$ is given in Chapter 18 as where\[c=e^{-r T}\left[F_{0} N\left(d_{1}ight)-K
Show that the $\operatorname{GARCH}(1,1)$ model $\sigma_{n}^{2}=\omega+\alpha u_{n-1}^{2}+\beta \sigma_{n-1}^{2}$ in equation (23.9) is equivalent to the stochastic volatility model \(d
Explain the difference between risk-neutral and real-world default probabilities.
Calculate all the fixed cash flows and their exact timing for the swap in Business Snapshot 33.1. Assume that the day count conventions are applied using target payment dates rather than actual
Explain carefully why a bank might choose to discount cash flows on a currency swap at a rate slightly different from LIBOR.
A company caps three-month LIBOR at 10% per annum. The principal amount is $20 million. On a reset date three-month LIBOR is 12% per annum. What payment would this lead to under the cap? When would
Explain the features of (a) callable and (b) puttable bonds.
Suppose you buy a Eurodollar call futures option contract with a strike price of 97.25. You exercise when the underlying Eurodollar futures price is 98.12. What is the payoff?
Calculate the price of an option that caps the 3-month rate starting in 18 months’ time at 13% (quoted with quarterly compounding) on a principal amount of $1,000. The forward interest rate for the
What are the advantages of term structure models over Black’s model for valuing interest rate derivatives?
Use the DerivaGem software to value a five-year collar that guarantees that the maximum and minimum interest rates on a LIBOR-based loan (with quarterly resets) are 7% and 5%, respectively. All
What is the value of a cash-or-nothing call that promises to pay $100 if the price of a non-dividend-paying stock is above $50 in three months? The current stock price is $50, the risk-free rate is
List eight types of barrier options.
How does an equity swap work?
Explain the relationship between a cancelable swap and a swap option.
The Canadian dollar LIBOR rate is 0.5% higher than the U.S. LIBOR rate for all maturities.A trader thinks that the spread between three-month U.S. LIBOR and three-month Canadian LIBOR will widen, but
How does a binary credit default swap differ from a regular credit default swap?
A credit default swap requires a semiannual payment at the rate of 60 basis points per year. The principal is $300 million and the credit default swap is settled in cash. A default occurs after four
Explain how a credit default swap is settled.
Explain how a cash CDO and a synthetic CDO are created.
Why can the pricing of a weather derivatives contract and a CAT bond be based on probabilities calculated from historical data?
A bank quotes an interest rate of 14% per annum with quarterly compounding. What is the equivalent rate with (a) continuous compounding and (b) annual compounding?
What is meant by LIBOR?
The six-month and one-year zero rates are both 10% per annum. For a bond that has a life of 18 months and pays a coupon of 8% per annum semiannually (with a coupon payment having just been made), the
Assuming that risk-free zero rates are as in Problem 4.5, what is the value of an FRA that enables the holder to pay LIBOR and receive 9.5% for a three-month period starting in one year on a
The term structure of interest rates is upward sloping. Put the following in order of magnitude:a. The five-year zero rateb. The yield on a five-year coupon-bearing bondc. The forward rate
A five-year bond provides a coupon of 5% per annum payable semiannually. Its price is 104. What is the bond’s yield? You may find Excel’s Solver useful.
The 6-month, 12-month. 18-month, and 24-month risk-free zero rates are 4%, 4.5%, 4.75%, and 5% with semiannual compounding.(a) What are the rates with continuous compounding?(b) What is the forward
Estimate the difference between short-term interest rates in Japan and the United States on May 13, 2015, from the information in Table 5.4.Data from Table 5.4. Table 5.4 Futures quotes for a
The spot price of oil is $80 per barrel and the cost of storing a barrel of oil for one year is$3, payable at the end of the year. The risk-free interest rate is 5% per annum continuously compounded.
It is January 9, 2017. The price of a Treasury bond with a 12% coupon that matures on October 12, 2030, is quoted as 102-07. What is the cash price?
It is May 5, 2017. The quoted price of a U.S. government bond with a 12% coupon that matures on July 27, 2024, is 110-17. What is the cash price?
It is July 30, 2017. The cheapest-to-deliver bond in a September 2017 Treasury bond futures contract is a 13% coupon bond, and delivery is expected to be made on September 30, 2017. Coupon payments
An investor is looking for arbitrage opportunities in the Treasury bond futures market.What complications are created by the fact that the party with a short position can choose to deliver any bond
Between October 30, 2017, and November 1, 2017, you have a choice between owning a U.S. government bond paying a 12% coupon and a U.S. corporate bond paying a 12%coupon. Consider carefully the day
Assume that a bank can borrow or lend money at the same interest rate in the LIBOR market. The 90-day rate is 10% per annum, and the 180-day rate is 10.2% per annum, both expressed with continuous
Company X wishes to borrow U.S. dollars at a fixed rate of interest. Company Y wishes to borrow Japanese yen at a fixed rate of interest. The amounts required by the two companies are roughly the
Explain what a seven-year swap rate is.
Explain the difference between the credit risk and the market risk in a financial contract.
Why is the expected loss to a bank from a default on a swap with a counterparty less than the expected loss from the default on a loan to the counterparty when the loan and swap have the same
(a) Company A has been offered the swap quotes in Table 7.3. It can borrow for three years at 3.45%. What floating rate can it swap this fixed rate into?(b) Company B has also been offered the swap
(a) Company X has been offered the swap quotes in Table 7.3. It can invest for four years at 2.8%. What floating rate can it swap this fixed rate into?(b) Company Y has also been offered the swap
In an interest rate swap, a financial institution has agreed to pay 3.6% per annum and to receive three-month LIBOR in return on a notional principal of $100 million with payments being exchanged
Suppose that the term structure of risk-free interest rates is flat in the United States and Australia. The USD interest rate is 7% per annum and the AUD rate is 9% per annum.The current value of the
The five-year swap rate when cash flows are exchanged semiannually is 4%. A company wants a swap where it receives payments at 4.2% per annum on a principal of $10 million.The OIS zero curve is flat
Add rows in Table 8.1 corresponding to losses on the underlying assets of(a) 2%,(b) 6%,(c) 14%, and(d) 18%.Data from Table 8.1 Table 8.1 Estimated losses to tranches of ABS CDO in Figure 8.3 Losses
Explain why brokers require margin when clients write options but not when they buy options.
“Employee stock options are different from regular exchange-traded stock options because they can change the company’s capital structure.” Explain this statement.
Explain why an American call option on a dividend-paying stock is always worth at least as much as its intrinsic value. Is the same true of a European call option? Explain your answer.
The price of a non-dividend paying stock is $19 and the price of a three-month European call option on the stock with a strike price of $20 is $1. The risk-free rate is 4% per annum.What is the price
Call options on a stock are available with strike prices of $15, $17 1/2, and $20 and expiration dates in three months. Their prices are $4, $2, and $1/2 , respectively. Explain how the options can
A foreign currency is currently worth $0.64. A one-year butterfly spread is set up using European call options with strike prices of $0.60, $0.65, and $0.70. The risk-free interest rates in the
A stock price is currently $40. It is known that at the end of one month it will be either$42 or $38. The risk-free interest rate is 8% per annum with continuous compounding.What is the value of a
A stock price is currently $50. It is known that at the end of six months it will be either$45 or $55. The risk-free interest rate is 10% per annum with continuous compounding.What is the value of a
For the situation considered in Problem 12.5, what is the value of a one-year European put option with a strike price of $100? Verify that the European call and European put prices satisfy put–call
What are the formulas for u and d in terms of volatility?
Explain how risk-neutral valuation could be used to derive the Black–Scholes–Merton formulas.
What is meant by implied volatility? How would you calculate the volatility implied by a European put option price?
What is Black’s approximation for valuing an American call option on a dividend-paying stock?
A currency is currently worth $0.80. Over each of the next two months it is expected to increase or decrease in value by 2%. The domestic and foreign risk-free interest rates are 6% and 8%,
A futures price is currently 50. At the end of six months it will be either 56 or 46. The risk-free interest rate is 6% per annum. What is the value of a six-month European call option on the futures
Suppose you buy a put option contract on October gold futures with a strike price of$1,200 per ounce. Each contract is for the delivery of 100 ounces. What happens if you exercise when the October
Suppose you sell a call option contract on April live cattle futures with a strike price of 140 cents per pound. Each contract is for the delivery of 40,000 pounds. What happens if the contract is
Can the vega of a derivatives portfolio be changed by taking a position in the underlying asset? Explain your answer.
Explain why portfolio insurance may have played a part in the stock market crash of October 19, 1987.
The probability for an up-movement on a binomial tree is (a − d)/(u − d). Explain how the growth factor a is calculated for(a) a non-dividend-paying stock,(b) a stock index,(c) a foreign
Explain the problem in using Monte Carlo simulation to value an American option.
Explain the historical simulation method for calculating VaR.

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