What is meant by the ‘‘delta’’ of a stock option?
> Explain the arbitrage opportunities in Problem 11.14 if the European put price is $3. Data from Problem 11.14: The price of a European call that expires in six months and has a strike price of $30 is $2. The underlying stock price is $29, and a dividend
> Describe the terminal value of the following portfolio: a newly entered-into long forward contract on an asset and a long position in a European put option on the asset with the same maturity as the forward contract and a strike price that is equal to th
> Give an intuitive explanation of why the early exercise of an American put becomes more attractive as the risk-free rate increases and volatility decreases.
> A 1-month European put option on a non-dividend-paying stock is currently selling for $2:50. The stock price is $47, the strike price is $50, and the risk-free interest rate is 6% per annum. What opportunities are there for an arbitrageur?
> Why do you think the increase in house prices during the 2000 to 2007 period is referred to as a bubble?
> Portfolio A consists of a 1-year zero-coupon bond with a face value of $2,000 and a 10-year zero-coupon bond with a face value of $6,000. Portfolio B consists of a 5.95-year zero-coupon bond with a face value of $5,000. The current yield on all bonds is
> Six-month LIBOR is 5%. LIBOR forward rates for the 6- to 12-month period and for the 12- to 18-month period are 5.5%. Swap rates for 2- and 3-year semiannual pay swaps are 5.4% and 5.6%, respectively. Estimate the LIBOR forward rates for for 18 months to
> A futures price is currently 40. It is known that at the end of three months the price will be either 35 or 45. What is the value of a three-month European call option on the futures with a strike price of 42 if the risk-free interest rate is 7% per annu
> Suppose that in Example 3.2 of Section 3.3 the company decides to use a hedge ratio of 0.8. How does the decision affect the way in which the hedge is implemented and the result?
> A 4-month European call option on a dividend-paying stock is currently selling for $5. The stock price is $64, the strike price is $60, and a dividend of $0.80 is expected in 1 month. The risk-free interest rate is 12% per annum for all maturities. What
> ‘‘When a futures contract is traded on the floor of the exchange, it may be the case that the open interest increases by one, stays the same, or decreases by one.’’ Explain this statement.
> Suppose that a European call option to buy a share for $100.00 costs $5.00 and is held until maturity. Under what circumstances will the holder of the option make a profit? Under what circumstances will the option be exercised? Draw a diagram illustratin
> A corporate treasurer is designing a hedging program involving foreign currency options. What are the pros and cons of using (a) NASDAQ OMX and (b) the over-the counter market for trading?
> ‘‘Employee stock options issued by a company are different from regular exchangetraded call options on the company’s stock because they can affect the capital structure of the company.’’ Explain this statement.
> Suppose that a European put option to sell a share for $60 costs $8 and is held until maturity. Under what circumstances will the seller of the option (the party with the short position) make a profit? Under what circumstances will the option be exercise
> Explain why margin accounts are required when clients write options but not when they buy options.
> Suppose that USD/sterling spot and forward exchange rates are as follows: What opportunities are open to an arbitrageur in the following situations? (a) A 180-day European call option to buy £1 for $1.52 costs 2 cents. (b) A 90-day European
> A U.S. investor writes five naked call option contracts. The option price is $3.50, the strike price is $60.00, and the stock price is $57.00. What is the initial margin requirement?
> What is a mezzanine tranche?
> An index is 1,200. The three-month risk-free rate is 3% per annum and the dividend yield over the next three months is 1.2% per annum. The six-month risk-free rate is 3.5% per annum and the dividend yield over the next six months is 1% per annum. Estimat
> Imagine you are the treasurer of a Japanese company exporting electronic equipment to the United States. Discuss how you would design a foreign exchange hedging strategy and the arguments you would use to sell the strategy to your fellow executives.
> What was the role of GNMA (Ginnie Mae) in the mortgage-backed securities market of the 1970s?
> Under what circumstances are (a) a short hedge and (b) a long hedge appropriate?
> Explain carefully the difference between selling a call option and buying a put option.
> Add rows in Table 8.1 corresponding to losses on the underlying assets of (a) 2%, (b) 6%, (c) 14%, and (d) 18%. Table 8.1 Estimated losses to tranches of ABS CDO in Figure 8.3. Losses on Losses to Losses to Losses to Losses to underlying mezzanine tr
> What differences exist in the way prices are quoted in the foreign exchange futures market, the foreign exchange spot market, and the foreign exchange forward market?
> What is the difference between the operation of the margin accounts administered by a clearing house and those administered by a broker?
> A company has issued a 3-year convertible bond that has a face value of $25 and can be exchanged for two of the company’s shares at any time. The company can call the issue, forcing conversion, when the share price is greater than or equal to $18. Assumi
> Suppose that in September 2018 a company takes a long position in a contract on May 2019 crude oil futures. It closes out its position in March 2019. The futures price (per barrel) is $48.30 when it enters into the contract, $50.50 when it closes out its
> Explain how CCPs work. What are the advantages to the financial system of requiring CCPs to be used for all standardized derivatives transactions between financial institutions?
> What is a subprime mortgage?
> Data for a number of stock indices are provided on the author’s Web site: http://www-2.rotman.utoronto.ca/~hull/data Choose an index and test whether a three standard deviation down movement happens more often than a three standard deviation up movement
> It is July 2017. 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 year. Futures contracts on gold are available with delive
> What is the price of a European put option on a non-dividend-paying stock when the stock price is $69, the strike price is $70, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is 6 months?
> Construct a table showing the payoff from a bull spread when puts with strike prices K1 and K2, with K2 > K1, are used.
> A trader owns a commodity that provides no income and has no storage costs as part of a long-term investment portfolio. The trader can buy the commodity for $1,250 per ounce and sell it for $1,249 per ounce. The trader can borrow funds at 6% per year and
> What is the price of a European call option on a non-dividend-paying stock when the stock price is $52, the strike price is $50, the risk-free interest rate is 12% per annum, the volatility is 30% per annum, and the time to maturity is 3 months?
> What does the Black–Scholes–Merton stock option pricing model assume about the probability distribution of the stock price in one year? What does it assume about the probability distribution of the continuously compounded rate of return on the stock duri
> Explain why the AAA-rated tranche of an ABS CDO is more risky than the AAA-rated tranche of an ABS.
> Suppose that G is a function of a stock price S and time. Suppose that and are the volatilities of S and G. Show that, when the expected return of S increases by , the growth rate of G increases by , where is a constant.
> 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 (excluding the initial investment
> Suppose that x is the yield to maturity with continuous compounding on a zero-coupon bond that pays off $1 at time T. Assume that x follows the process where a, , and s are positive constants and dz is a Wiener process. What is the process followed by
> Explain why the market maker’s bid–offer spread represents a real cost to options investors.
> Suppose that a stock price S follows geometric Brownian motion with expected return µ and volatility σ: What is the process followed by the variable Sn? Show that Sn also follows geometric Brownian motion.
> A cattle farmer expects to have 120,000 pounds of live cattle to sell in 3 months. The live cattle futures contract traded by the CME Group is for the delivery of 40,000 pounds of cattle. How can the farmer use the contract for hedging? From the farmer’s
> A call with a strike price of $60 costs $6. A put with the same strike price and expiration date costs $4. Construct a table that shows the profit from a straddle. For what range of stock prices would the straddle lead to a loss?
> Consider the situation in which stock price movements during the life of a European option are governed by a two-step binomial tree. Explain why it is not possible to set up a position in the stock and the option that remains riskless for the whole of th
> What are the formulas for u and d in terms of volatility?
> A company that is uncertain about the exact date when it will pay or receive a foreign currency may try to negotiate with its bank a forward contract that specifies a period during which delivery can be made. The company wants to reserve the right to cho
> It is July 16. A company has a portfolio of stocks worth $100 million. The beta of the portfolio is 1.2. The company would like to use the December futures contract on a stock index to change the beta of the portfolio to 0.5 during the period July 16 to
> Explain why an American option is always worth at least as much as its intrinsic value.
> ‘‘Speculation in futures markets is pure gambling. It is not in the public interest to allow speculators to trade on a futures exchange.’’ Discuss this viewpoint.
> Explain why an American option is always worth at least as much as a European option on the same asset with the same strike price and exercise date.
> Suppose that a bank buys an option from a client. The option is uncollateralized and there are no other transactions outstanding with the client. The expected values of the option at the midpoint of years 1, 2, and 3 are 6, 5, and 4. The probability of t
> Calculate u, d, and p when a binomial tree is constructed to value an option on a foreign currency. The tree step size is 1 month, the domestic interest rate is 5% per annum, the foreign interest rate is 8% per annum, and the volatility is 12% per annum.
> A stock index currently stands at 300 and has a volatility of 20%. The risk-free interest rate is 8% and the dividend yield on the index is 3%. Use a three-step binomial tree to value a six-month put option on the index with a strike price of 300 if it i
> Explain what KVA measures.
> Explain the difference between the views of financial economists and most practitioners on how MVA and FVA should be calculated.
> (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 been offered the swap quotes in Table 7.3. It can borrow for five years at LIBOR
> Verify that DerivaGem agrees with the price of the bond in Section 4.6. Test how well DV01 predicts the effect of a 1-basis-point increase in all rates. Estimate the duration of the bond from DV01. Use DV01 and Gamma to predict the effect of a 200-basis-
> Explain what MVA and FVA measure.
> ‘‘If most of the call options on a stock are in the money, it is likely that the stock price has risen rapidly in the last few months.’’ Discuss this statement.
> Can a trading rule based on the past history of a stock’s price ever produce returns that are consistently above average? Discuss.
> Explain the meaning of “netting”. Suppose no collateral is posted. Why does a netting agreement usually reduce credit risks to both sides? Under what circumstances does netting have no effect on credit risk?
> A company is trying to decide between issuing debt and equity to fulfill a funding need. What in theory should happen to the return required by equity holders if it chooses (a) debt and (b) equity?
> What is meant by the term ‘‘agency costs’’? How did agency costs play a role in the credit crisis?
> The following table gives the prices of bonds: (a) Calculate zero rates for maturities of 6 months, 12 months, 18 months, and 24 months. (b) What are the forward rates for the following periods: 6 months to 12 months, 12 months to 18 months, and 18 month
> Show that, if the futures price of a commodity is greater than the spot price during the delivery period, then there is an arbitrage opportunity. Does an arbitrage opportunity exist if the futures price is less than the spot price? Explain your answer.
> The 6-month, 12-month, 18-month, and 24-month 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 rate for the 6-month period beginning in 18 months? (c) What is
> It is now October 2017. A company anticipates that it will purchase 1 million pounds of copper in each of February 2018, August 2018, February 2019, and August 2019. The company has decided to use the futures contracts traded by the CME Group to hedge it
> Explain how the ‘‘cure period’’ is used in the calculation of CVA.
> What is the difference between the over-the-counter market and the exchange-traded market? What are the bid and offer quotes of a market maker in the over-the-counter or exchange-traded market?
> Use equation (22.1) to show that when the loss distribution is normal, VaR with 99% confidence is almost exactly the same as ES with 97.5% confidence. equation (22.1) ES = u+a- (22.1)| 27 (1 – X)
> The treasurer of a corporation is trying to choose between options and forward contracts to hedge the corporation’s foreign exchange risk. Discuss the advantages and disadvantages of each.
> An American put option to sell a Swiss franc for dollars has a strike price of $0.80 and a time to maturity of 1 year. The Swiss franc’s volatility is 10%, the dollar interest rate is 6%, the Swiss franc interest rate is 3%, and the current exchange rate
> Calculate the price of a six-month European put option on the spot value of the S&P 500. The six-month forward price of the index is 1,400, the strike price is 1,450, the risk-free rate is 5%, and the volatility of the index is 15%.
> A call option with a strike price of $50 costs $2. A put option with a strike price of $45 costs $3. Explain how a strangle can be created from these two options. What is the pattern of profits from the strangle?
> Explain the no-arbitrage and risk-neutral valuation approaches to valuing a European option using a one-step binomial tree.
> The futures price of a commodity is $90. Use a three-step tree to value (a) a 9-month American call option with strike price $93 and (b) a 9-month American put option with strike price $93. The volatility is 28% and the risk-free rate (all maturities) is
> Explain the difference between the credit risk and the market risk in a financial contract.
> A stock index is currently 1,500. Its volatility is 18%. The risk-free rate is 4% per annum (continuously compounded) for all maturities and the dividend yield on the index is .5%. Calculate values for u, d, and p when a 6-month time step is used. What i
> The volatility of a non-dividend-paying stock whose price is $78, is 30%. The risk-free rate is 3% per annum (continuously compounded) for all maturities. Calculate values for u, d, and p when a 2-month time step is used. What is the value a 4-month Euro
> Explain how margin accounts protect futures traders against the possibility of default.
> Suppose you call your broker and issue instructions to sell one July hogs contract. Describe what happens.
> Calculate the implied volatility of soybean futures prices from the following information concerning a European put on soybean futures: Current futures price Exercise price Risk-free rate 525 525 6% per annum 5 months Time to maturity Put price 20
> Explain carefully the difference between writing a put option and buying a call option.
> For the situation considered in Problem 13.12, what is the value of a 6-month European put option with a strike price of $51? Verify that the European call and European put prices satisfy put–call parity. If the put option were American, would it ever be
> OIS rates have been estimated as 3.4% for all maturities. The three-month LIBOR rate is 3.5%. For a six-month swap where payments are exchanged every three months the swap rate is 3.6%. All rates are expressed with quarterly compounding. What is the LIBO
> A stock price is currently $50. Over each of the next two 3-month periods it is expected to go up by 6% or down by 5%. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a 6-month European call option with a str
> Suppose that 3-month, 6-month, 12-month, 2-year, and 3-year OIS rates are 2.0%, 2.5%, 3.2%, 4.5%, and 5%, respectively. The 3-month, 6-month, and 12-month OISs involve a single exchange at maturity; the 2-year and 3-year OISs involve quarterly exchanges.
> A stock price is currently $40. It is known that at the end of 3 months it will be either $45 or $35. The risk-free rate of interest with quarterly compounding is 8% per annum. Calculate the value of a 3-month European put option on the stock with an exe
> A stock price is currently $80. It is known that at the end of 4 months it will be either $75 or $85. The risk-free interest rate is 5% per annum with continuous compounding. What is the value of a 4-month European put option with a strike price of $80?
> A stock price is currently $40. It is known that at the end of 1 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 1-month European call option with a strike price of $39?
> A currency swap has a remaining life of 15 months. It involves exchanging interest at 10% on £20 million for interest at 6% on $30 million once a year. The term structure of riskfree interest rates in the United Kingdom is flat at 7% and the term structu
> Explain how an aggressive bear spread can be created using put options.
> Use put–call parity to relate the initial investment for a bull spread created using calls to the initial investment for a bull spread created using puts.
> Explain what CVA and DVA measure.
> A trader buys a call option with a strike price of $45 and a put option with a strike price of $40. Both options have the same maturity. The call costs $3 and the put costs $4. Draw a diagram showing the variation of the trader’s profit with the asset pr
> What is the difference between a strangle and a straddle?
> What is meant by a protective put? What position in call options is equivalent to a protective put?
