Option Pricing & Risk Management Mock Final Exam
A project whose operation can be switched on and off is worth more than a similar project without this flexibility. The cost of restarting (or shutting down) operations may be thought of as the exercise price. T or F
TRUE
In real options, the required investment is considered the exercise price T or F
TRUE
The price of a European call option on a stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% and the time to maturity is one year. A dividend of $1 is expected in six months. What is the price of a one-year European put option on the stock with a strike price of $50? a. $8.97 b. $6.97 c. $3.06 d. $1.12
c. $3.06 Put-call parity is c+Ke-rT = p+S0. In this case K = 50, S0 = 51, r = 0.06, T = 1, and c = 6. The present value of the dividend is 1×e−0.06×0.5 = 0.97. It follows that p = 6+50e-0.06×1 − (51- 0.97) = 3.06.
Managers who hold real options should view: a. Themselves as passive onlookers with no decision making opportunities. b. Real options as tools for reducing the total risk of the firm through diversification. c. Real options as opportunities to alter management decisions in the future. d. Themselves as agents who are looking for higher compensation.
c. Real options as opportunities to alter management decisions in the future.
A project is worth $12 million today without an abandonment option. Suppose the value of the project is either $18 million one year from today (if product demand is high) or $8 million (if product demand is low). It is possible to sell off the project for $10 million if product demand is low. Calculate the value of the abandonment option if the discount rate is 5% per year. a. $1.03 million b. $0.88 million c. $1.90 million d. $5.14 million
a. $1.03 million 12 = (18 * p) + (8 *( 1 - p)) / 1.05 p = 046; (1 - p) = 0.54 Put = (0.46 *$0) + (0.54 * $2M) / 1.05 = $1.03 M
A trader creates a long butterfly spread from options with strike prices $60, $65, and $70 by trading a total of 400 options. The options are worth $11, $14, and $18. What is the maximum net loss (after the cost of the options is taken into account)? a. $100 b. $200 c. $300 d. $400
a. $100 The butterfly spread involves buying 100 options with strike prices $60 and $70 and selling 200 options with strike price $65. The maximum loss is when the stock price is less than $60 or greater than $70. The total payoff is then zero. The cost of setting up the butterfly spread is 11×100+18×100−14×200 = $100. The loss is therefore $100.
(Challenge question) The current price of a non-dividend paying stock is $30. Use a twostep tree to value a European put option on the stock with a strike price of $32 that expires in 6 months with u = 1.1 and d = 0.9. Each step is 3 months, the risk free rate is 8%. a. $2.24 b. $2.44 c. $2.64 d. $2.84
a. $2.24 The probability of an up movement is: p = (e^-r*T - d)/(u-d) = 0.6010 **Build a 3 step binomial tree
When the non-dividend paying stock price is $25, the strike price is $30, the risk-free rate is 5%, the volatility is 30% and the time to maturity is 2 years, which of the following is the price of a European call option on the stock? a. $3.39 b. $9.03 c. $8.54 d. $5.30
a. $3.39 Solve using the Put-Call Parity Call = S * N(d1) - K * e^ -r*T * N(d22)
On March 1 a commodity's spot price is $60 and its August futures price is $59. On July 1 the spot price is $64 and the August futures price is $63.50. A company entered into futures contracts on March 1 to hedge its purchase of the commodity on July 1. It closed out its position on July 1. What is the effective price (after taking account of hedging) paid by the company? a. $59.50 b. $60.50 c. $61.50 d. $63.50
a. $59.50 The user of the commodity takes a long futures position. The gain on the futures contract is 63.50−59 or $4.50. The effective price realized is therefore 64−4.50 or $59.50. This can also be calculated as the March 1 futures price (=59) plus the basis on July 1 (=0.50).
The current spot rate is BP 0.5024/$US. The 3-month forward rate is BP 0.5040/$US. The TE Company expects a payment of BP 100 million in three months. If the firm hedges this transaction in the forward market, what is the $US amount it will receive in three months? a. $US198.41 million b. $US199.04 million c. $US 50.40 million d. $US 50.24 million
a. $US198.41 million $US amount = 100/0.504 = 198.41
Company X and Company Y have been offered the following rates Fixed Rate Floating Rate Company X 3.5% 3-month LIBOR + 10bp Company Y 4.5% 3-month LIBOR + 30bp Suppose that Company X borrows fixed and company Y borrows floating. If they enter into a swap with each other where the apparent benefits are shared equally, what is company X's effective borrowing rate? a. 3-month LIBOR−30bp b. 3.1% c. 3-month LIBOR−10bp d. 3.3%
a. 3-month LIBOR−30bp The interest rate differential between the fixed rates is 100 basis points. The interest rate differential between the floating rates is 20 basis points. The difference between the interest rates differentials is 100 - 20 = 80 basis points. This is the total apparent gain from the swap to the two sides. Since the benefits are shared equally company X should be able to borrow at 40 bp less than it is currently offered in the floating rate market, i.e., at LIBOR minus 30 bp.
The seller of a forward contract agrees to: a. Deliver a product at a later date for a price set today. b. Receive a product at a later date at the price on that later date. c. Receive a product at a later date for a price set today. d. Deliver a product at a later date for a price set on that later date.
a. Deliver a product at a later date for a price set today.
Which of the following is NOT true about forward and futures contracts? a. Forward contracts are more liquid than futures contracts. b. The futures contracts are traded on exchanges while forward contracts are traded in the over-the-counter market. c. In theory forward prices and futures prices are equal when there is no uncertainty about future interest rates. d. Taxes and transaction costs can lead to forward and futures prices being different.
a. Forward contracts are more liquid than futures contracts. Futures contracts are more liquid than forward contracts. To unwind a futures position it is simply necessary to take an offsetting position. The statements in B, C, and D are correct.
Which of the following statements is false? a. Increasing the pay-for-performance sensitivity comes with the added benefit of reducing manager's risk. b. Stock and option grants give managers a direct incentive to increase the stock price to make their stock or options as valuable as possible. c. By tying compensation to performance, the shareholders effectively give the manager an ownership stake in the firm. d. During the 1990s, most companies adopted compensation policies that more directly gave managers an ownership stake by including grants of stock or stock options to executives.
a. Increasing the pay-for-performance sensitivity comes with the added benefit of reducing manager's risk. Increasing the pay-for-performance sensitivity comes at the cost of burdening managers with risk.
You own a small networking startup. You have just received an offer to buy your firm from a large, publicly traded firm, JCH Systems. Under the terms of the offer, you will receive 1 million shares of JCH. JCH stock currently trades for $25 per share. You can sell the shares of JCH that you will receive in the market at any time. But as part of the offer, JCH also agrees that at the end of the next year, it will buy the shares back from you for $25 per share if you desire. Suppose the current one-year risk-free rate is 6.00%, the volatility of JCH stock is 30%, and JCH does not pay dividends. a. Is this offer worth more than $25 million? Explain. b. What is the value of the offer?
a. The offer is worth more than $25 million because of the put option. b. The value of the offer is the current value of the shares plus the value of the put option. To calculate the value of the call using the B-S Model: S = $25.00 K = $25.00 σ = 0.30 T = 1.0 rf = 0.06 Put = Call + K * e-r*T - S = $3.68 + $25.00e^-.06*1 - $25.00 = $2.22 So, the value of the offer is 25 + 2.22 = $27.22 million.
Which of the following best describes the intrinsic value of an option? a. The value it would have if the owner had to exercise it immediately or not at all. b. The Black-Scholes-Merton price of the option. c. The lower bound for the option's price. d. The amount paid for the option.
a. The value it would have if the owner had to exercise it immediately or not at all. The intrinsic value of an option is the value it would have if it were about the expire which is the same as the value in A.
You sell two December futures contracts when the futures price is $1,010 per unit. Each contract is on 100 units and the initial margin per contract that you provide is $2,000. The maintenance margin per contract is $1,500. During the next day the futures price rises to $1,012 per unit. What is the balance of your margin account at the end of the day? a. $1,800 b. $3,600 c. $2,200 d. $4,400
b. $3,600 The price has increased by $2. Because you have a short position you lose 2×100 or $200 per contract, or $400 overall. The balance in the margin account therefore goes down from $4,000 to $3,600.
If a Big Mac costs $C3.00 in Canada and $2.31 in the U.S., according to purchasing power parity, what is the implied exchange rate in terms of $C/$US? a. 1.3793 b. 1.2987 c. 1.3276 d. 0.7700
b. 1.2987 $C/$US = 3.00/2.31 = 1.2987.
The spot Yen/US dollar exchange rate is 119.795 Yen/$US. The 3-month forward rate is 118.397 Yen/$US. What is the Yen's forward premium (or discount) on the dollar, expressed as an annual percentage? a. 6.5% discount b. 4.7% premium c. 6.5% premium d. 4.7% discount
b. 4.7% premium Forward (premium or discount) = 4[(119.795/118.397) - 1] = + 4.7% = 4.7% premium.
The option to abandon (or sell) a project, such as the right to abandon a coal mine, is most similar to: a. A swap contract. b. A put option on a stock. c. A call option on a stock. d. A futures contract on a bond
b. A put option on a stock.
A company surprises the market with an announcement that it has granted stock options to senior executives. The options are exercised four years later. When does dilution take place? a. Dilution takes place when the options are exercised b. Dilution takes place on the announcement date c. Dilution takes place gradually over the four years d. There is no dilution
b. Dilution takes place on the announcement date Efficient markets should ensure that dilution takes place at the time of the announcement.
Which of the following is NOT usually true about employee stock options? a. There is a vesting period. b. They can be sold to other employees. c. They are often at-the-money when issued. d. Their value is currently a charge to the income statement.
b. They can be sold to other employees. Employee stock options cannot be sold. A, C, and D are true.
When a firm hedges a risk it: a. Eliminates the risk. b. Transfers the risk to someone else. c. Makes the government assume the risk. d. Increases the risk.
b. Transfers the risk to someone else.
Six-month call options with strike prices of $35 and $40 cost $6 and $4, respectively. What is the maximum gain when a bull spread is created by trading a total of 200 options? a. $100 b. $200 c. $300 d. $400
c. $300 The bull spread involves buying 100 calls with strike $35 and selling 100 calls with strike price $40. The cost is 6×100−4×100=$200. The maximum payoff (when the stock price is greater than or equal to $40 is $500. The maximum gain is therefore 500 −200 = $300.
Which of the following ensures that managers are rewarded only when a company performs better than its competitors? a. A constant strike price for executive stock options. b. A strike price that increases with time. c. A strike price that changes in line with an index of stock prices. d. A strike price that is tied to reported profit.
c. A strike price that changes in line with an index of stock prices. If an option is initially at the money and the strike price increases in line with an index, the company must outperform the index for the option to move in the money.
The current price of a non-dividend-paying stock is $40. Over the next year it is expected to rise to $42 or fall to $37. An investor buys put options with a strike price of $41. Which of the following is necessary to hedge the position? a. Buy 0.2 shares for each option purchased. b. Sell 0.2 shares for each option purchased. c. Buy 0.8 shares for each option purchased. d. Sell 0.8 shares for each option purchased.
c. Buy 0.8 shares for each option purchased. The payoff from the put option is zero if there is an up movement and 4 if there is a down movement. Suppose that the investor buys one put option and buys ∆ shares. If there is an up movement the value of the portfolio is ∆×42. If there is a down movement it is worth ∆×37+4. These are equal when 37∆+4=42∆ or ∆=0.8. The investor should therefore buy 0.8 shares for each option purchased.
When interest rates increase with all else remaining the same, which of the following is true? a. Both calls and puts increase in value. b. Both calls and puts decrease in value. c. Calls increase in value while puts decrease in value. d. Puts increase in value while calls decrease in value
c. Calls increase in value while puts decrease in value Calls increase and puts decrease in value. As explained in the text an increase in interest rates causes the growth rate of the stock price to increase and the discount rate to increase. An increase in interest rates therefore reduces the value of puts because puts are hurt by both a discount rate increase and a growth rate increase. For calls it turns out that the growth rate increase is more important than the discount rate increase so that their values increase when interest rates increase. (Note that we are assuming all else equal and so the asset price does not change.)
Your U.S.-based firm is deciding between using currency futures contracts or a forward contract with its commercial bank in order to hedge a scheduled dividend from its subsidiary corporation in Germany. The dividend will be repatriated in July, while the currency futures contracts are only available for June or September delivery. Which of the following choices properly hedges the transaction without basis risk? a. Long Euro future contracts. b. Short Euro future contracts. c. Enter Forward to sell Euros forward in July. d. Enter Forward to buy Euros forward in July
c. Enter Forward to sell Euros forward in July.
Which of the following is NOT true? a. Management has an incentive to issue executive stock options after bad news. b. Management has an incentive to issue executive stock options before good news. c. Executive stock options with no vesting period encourage management to pursue strategies that are best for the company in the long run. d. Management have an incentive to time the announcement of good news just before they plan to exercise their stock options.
c. Executive stock options with no vesting period encourage management to pursue strategies that are best for the company in the long run. Executive stock options tend to cause management to have short-term horizons. A, B, and D are not true. This is because management want to issue options when the price is low and exercise when the price is high.
The price of a stock on February 1 is $48. A trader sells 200 put options (2 contracts) on the stock with a strike price of $40 when the option price is $2. The options are exercised when the stock price is $39. The trader's net profit or loss is: a. Loss of $800 b. Loss of $200 c. Gain of $200 d. Loss of $900
c. Gain of $200 The payoff is 40−39 or $1 per op on. For 200 options the payoff is therefore 1×200 or $200. However the premium received by the trader is 2×200 or $400. The trader therefore has a net gain of $200.
Which of the following statements is false? a. The shareholders as a group elect a board of directors to monitor managers. The directors themselves, however, have the same conflict of interest-monitoring is costly and in many cases directors do not get significantly greater benefits than other shareholders from monitoring the managers closely. b. In principle, the board of directors hires the executive team, sets its compensation, approves major investments and acquisitions, and dismisses executives if necessary. c. In the United States, the board of directors has a clear fiduciary duty to protect the interests of both the owners of the firm (the shareholders) and the interests of other stakeholders in the firm (such as the employees). d. When the ownership of a corporation is widely held, no one shareholder has an incentive to bear the cost of monitoring, because she bears the full cost of monitoring but the benefit is divided among all shareholders.
c. In the United States, the board of directors has a clear fiduciary duty to protect the interests of both the owners of the firm (the shareholders) and the interests of other stakeholders in the firm (such as the employees). In the United States, the board of directors has a clear fiduciary duty to protect the interests of the owners of the firm-the shareholders. Most other countries give some weight to the interests of other stakeholders in the firm, such as the employees.
Which of the following statements is false? a. New SEC rules require firms to report option grants within two days of the grant date, which may help prevent further abuses. b. Studies have found evidence that the practice of timing the release of information to maximize the value of CEO stock options is widespread. c. Managers have an incentive to manipulate the release of financial forecasts so that good news comes out before options are granted and bad news is delayed until after the options are granted. d. The factor contributing most to the climb in CEO total compensation for the 1990s was the sharp increase in the value of stock and options granted each year
c. Managers have an incentive to manipulate the release of financial forecasts so that good news comes out before options are granted and bad news is delayed until after the options are granted. Managers have an incentive to manipulate the release of financial forecasts so that bad news comes out before options are granted and good news comes out after options are granted.
Which of the following is true? a. Gold producers should always hedge the price they will receive for their production of gold over the next three years. b. Gold producers should always hedge the price they will receive for their production of gold over the next one year. c. The hedging strategies of a gold producer should depend on whether it shareholders want exposure to the price of gold. d. Gold producers can hedge by buying gold in the forward market.
c. The hedging strategies of a gold producer should depend on whether it shareholders want exposure to the price of gold. Some shareholders buy gold stocks to gain exposure to the price of gold. They do not want the company they invest in to hedge. In practice gold mining companies make their hedging strategies clear to shareholders.
A one-year call option on a stock with a strike price of $30 costs $3; a one-year put option on the stock with a strike price of $30 costs $4. Suppose that a trader buys two call options and one put option. The breakeven stock price below which the trader makes a profit is: a. $25 b. $28 c. $26 d. $20
d. $20 When the stock price is $20 the two call options provide no payoff. The put option provides a payoff of 30−20 or $10. The total cost of the option is 2×3+ 4 or $10. The stock price in D, $20, is therefore the breakeven stock price below which the position is profitable because it is the price for which the cost of the options equals the payoff.
An example of a real option is: a. The option to make follow-on investments. b. The option to abandon a project. c. The option to wait before investing. d. All of the options.
d. All of the options.
A type of risk peculiar to a forward contract is called: a. Market risk. b. Duration risk. c. Currency risk. d. Counterparty risk.
d. Counterparty risk.
In addition to bearing risk, insurance companies also bear: I) administrative costs; II) moral hazard costs; III) adverse selection costs a. I only b. II only c. III only d. I, II, and III
d. I, II, and III
Consider a put option and a call option with the same strike price and time to maturity. Which of the following is true? a. It is possible for both options to be in the money. b. It is possible for both options to be out of the money. c. One of the options must be in the money. d. One of the options must be either in the money or at the money
d. One of the options must be either in the money or at the money. If the stock price is greater than the strike price the call is in the money and the put is out of the money. If the stock price is less than the strike price the call is out of the money and the put is in the money. If the stock price is equal to the strike price both options are at the money.
. An investor has exchange-traded put options to sell 100 shares for $20. There is a 25% stock dividend. Which of the following is the position of the investor after the stock dividend? a. Put options to sell 100 shares for $20. b. Put options to sell 75 shares for $25. c. Put options to sell 125 shares for $15. d. Put options to sell 125 shares for $16.
d. Put options to sell 125 shares for $16 The stock dividend is equivalent to a 5 for 4 stock split. The number of shares goes up by 25% and the strike price is reduced to 4/5 of its previous value
When the Black-Scholes-Merton and binomial tree models are used to value an option on a non-dividend-paying stock, which of the following is true? a. The binomial tree price converges to a price slightly above the Black-Scholes-Merton price as the number of time steps is increased. b. The binomial tree price converges to a price slightly below the Black-Scholes-Merton price as the number of time steps is increased. c. Either A or B can be true. d. The binomial tree price converges to the Black-Scholes-Merton price as the number of time steps is increased.
d. The binomial tree price converges to the Black-Scholes-Merton price as the number of time steps is increased. The binomial tree valuation method and the Black-Scholes formula are based on the same set of assumptions. As the number of time steps is increased the answer given by the binomial tree approach converges to the answer given by the Black-Scholes-Merton formula.
Which of the following is NOT true about call and put options? a. An American option can be exercised at any time during its life. b. A European option can only be exercised on the maturity date. c. Investors must pay an upfront price (the option premium) for an option contract. d. The price of a call option increases as the strike price increases.
d. The price of a call option increases as the strike price increases A call option is the option to buy for the strike price. As the strike price increases this option becomes less attractive and is therefore less valuable. A, B, and C are true.