Q&A Hero

Q: What is the delta on a $25 strike put? Assume S = $24.00, σ = 0.35, r = 0.06, the stock pays a 2.0% continuous dividend and the option expires in 40 days? A) 0.582 B) 0.602 C) 0.662 D) 0.702

Q: What is the delta on a $20 strike call? Assume S = $22.00, σ = 0.30, r = 0.05, the stock pays a 1.0% continuous dividend and the option expires in 80 days? A) 0.790 B) 0.820 C) 0.850 D) 0.880

Q: What is the price of a $30 strike put? Assume S = $28.50, σ = 0.32, r = 0.04, the stock pays a 1.0% continuous dividend and the option expires in 110 days? A) $2.70 B) $2.10 C) $1.80 D) $1.20

Q: What is the price of a $25 strike call? Assume S = $23.50, σ = 0.24, r = 0.055, the stock pays a 2.5% continuous dividend and the option expires in 45 days? A) $0.60 B) $0.50 C) $0.40 D) $0.30

Q: What is the price of a $60 strike put? Assume S = $63.75, σ = 0.20, r = 0.055, the stock pays no dividend and the option expires in 50 days? A) $0.66 B) $0.55 C) $0.44 D) $0.33

Q: What is the price of a $35 strike call? Assume S = $38.50, σ = 0.25, r = 0.06, the stock pays no dividend and the option expires in 45 days. A) $3.50 B) $3.65 C) $3.80 D) $3.95

Q: Ask the class to prove that option pricing is consistent with standard discounted cash flow calculations. Propose that students form groups and develop two binomial trees for the same set of data. One tree should use real probabilities as defined in chapter 11 and the other as defined in chapter 10.

Q: When developing a binomial tree model where stocks pay discrete dividends, what problem may occur?

Q: What is the primary potential for error when using the Cox-Ross-Rubenstein binomial tree?

Q: In a binomial pricing model, what is the lowest price of an option at any node and why?

Q: What is the relationship between dividends and the forecasted stock price in a binomial model?

Q: Under what circumstances should an option be exercised early?

Q: Why is an American call option rarely exercised early, and thus priced similar to European options?A) Early exercise requires purchasing the stockB) Most option sellers cannot deliver the stockC) Option prices usually exceed intrinsic valuesD) Short sellers disrupt delivery

Q: What economic concept is central to proving that risk neutral pricing functions in the establishing of option prices? A) Consumption possibilities B) Factor analysis C) Marginal average cost D) Declining marginal utility

Q: Using a binomial pricing model, what is the impact on the price of a call option if the company increases the dividend paid to shareholders? The call option price: A) Will drop B) Will increase C) Will remain constant D) Impact cannot be determined

Q: A stock price is $85.00. Assume r = 0.07 and there is no dividend. What is the 6-month forward price? A) $88.03 B) $89.16 C) $90.26 D) $92.33

Q: Consider a three-period binomial model of 12 months. Assume the stock price is $37.50, σ = 0.20, r = 0.05 and the exercise price of a call option is $35. What is the forecasted price of the stock at the node after two consecutive upward movements of the stock price? A) $38.68 B) $42.80 C) $48.84 D) $50.06

Q: Consider a one-period binomial model of 12 months. Assume the stock price is $54.00, σ = 0.25, r = 0.04 and the exercise price of a call option is $55. What is the forecasted price of the stock given a downward movement during the year? A) $43.77 B) $ 45.28 C) $48.98 D) $51.84

Q: Consider a one-period binomial model of 12 months. Assume the stock price is $54.00, σ = 0.25, r = 0.04 and the exercise price of a call option is $55. What is the forecasted price of the stock given an upward movement during the year? A) $56.16 B) $61.01 C) $65.12 D) $72.16

Q: Consider a one-period binomial model of 6 months. Assume the stock price is $63.00, σ = 0.28, r = 0.05 and the stock's expected return is 14.0%. What is the true probability of the stock going up? A) 56.6% B) 52.4% C) 48.2% D) 46.4%

Q: Consider a one-period binomial model of 6 months. Assume the stock price is $45.00, σ = 0.20, r = 0.06 and the stock's expected return is 12.0%. What is the discount rate for a $45.00 strike European call option (Y)? A) 38.2% B) 39.1% C) 42.5% D) 45.6%

Q: Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $60.00, σ = 0.30, r = 0.05. An American put option with a strike price of $65 would be exercised early at what dividend yield? A) 5.0% B) 6.0% C) 11.0% D) Never exercised early

Q: Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $50.00, σ = 0.20, r = 0.06 and the dividend yield = 3.5%. What is the lowest strike price where early exercise would occur with an American put option? A) $50 B) $55 C) $60 D) $65

Q: Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $75.00, σ = 0.35, and r = 0.05. An American call option with a strike price of $80 would be exercised early at what dividend yield? A) 5.0% B) 7.0% C) 9.0% D) Never exercise early

Q: Consider a two-period binomial model, where each period is 6 months. Assume the stock price is $46.00, σ = 0.28, r = 0.06 and the dividend yield is 2.0%. What is the maximum approximate strike price where early exercise would occur with an American call option? A) $29 B) $33 C) $42 D) $46

Q: Discuss options on other assets. Ask students to define currency options, futures options, index options, and commodity options. Require that the students state which variables in the securities listed above correspond with the binomial pricing inputs used for stock options.

Q: Explain the impact a constant dividend yield would have on the price of a call option.

Q: Using a binomial tree explanation, explain the situation in which an American option would alter the pricing of an option.

Q: Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month put option, using 3-month intervals as the time period. K = $40.00, S = $37.90, r = 5.0%, σ = 0.35

Q: Draw the binomial tree listing only the stock prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $70, S = $68.50, r = 6.0%, σ = 0.32

Q: Draw the binomial tree listing only the option prices at each node. Assume the following data on a 6-month call option, using 3-month intervals as the time period. K = $40, S = $37.90, r = 5.0%, σ = 0.35

Q: For an option trading in the money, what is the likely impact on the binomial option price as the number of binomial steps is increased?A) The price will fallB) The price will increaseC) The price will remain constantD) The impact cannot be determined

Q: In the case of a 1-year option, the current stock price is $52 per share. If the stock price has an equal chance of ending the year at either $58 or $45, what is the â–³ given an interest rate of 6.0% and an exercise price of $50? A) 0.2145 B) 0.3254 C) 0.5411 D) 0.6154

Q: A call option has an exercise price of $30. The stock price at a point on the binomial tree is $36.24. The calculated present value of the option at that same point is $5.86. What figure should be used to calculate option prices at points moving toward the final price? A) $5.86 B) $6.24 C) $6.62 D) $7.01

Q: Using a binomial tree, what is the price of a $40 strike 6-month put option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, σ = 0.35 A) $3.52 B) $3.66 C) $3.84 D) $3.91

Q: Using a binomial tree, what is the price of a $40 strike 6-month call option, using 3-month intervals as the time period? Assume the following data: S = $37.90, r = 5.0%, σ = 0.35 A) $2.50 B) $2.76 C) $2.92 D) $3.08

Q: A stock is selling for $68.50. Interest rates are 6.0% and the returns on the stock have a standard deviation of 32.0%. What is the forecasted price of the stock using 3-month periods at Suudu? A) $74.08 B) $94.24 C) $100.17 D) $111.12

Q: A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over 6 months, assuming two periods of 3 months each? A) $64.96 B) $69.69 C) $73.48 D) $76.96

Q: A stock is selling for $53.20. Interest rates are 6.0% and the returns on the stock have a standard deviation of 24.0%. What is the forecasted up movement in the stock over a 6-month interval? A) $64.96 B) $69.69 C) $73.48 D) $76.96

Q: A stock is selling for $41.60. The strike price on a call, maturing in 6 months, is $45. The possible stock prices at the end of 6 months are $35.00 and $49.00. Interest rates are 5.0%. Given an under-priced option, what are the short sale proceeds in an arbitrage strategy? A) $6.36 B) $8.22 C) $10.43 D) $11.89

Q: A stock is selling for $18.50. The strike price on a call, maturing in 6 months, is $20. The possible stock prices at the end of 6 months are $22.50 and $15.00. Interest rates are 6.0%. How much money would you borrow to create an arbitrage on a call trading for $2.00? A) $2.54 B) $4.85 C) $6.60 D) $8.85

Q: The monthly standard deviation for a stock is 4.2%. What is the 6 month standard deviation for the security? A) 4.2 % B) 10.3 % C) 25.2 % D) 50.4 %

Q: A stock is selling for $32.70. The strike price on a call, maturing in 6 months, is $35. The possible stock prices at the end of 6 months are $39.50 and $28.40. If interest rates are 6.0%, what is the option price? A) $1.90 B) $2.80 C) $3.40 D) $4.20

Q: The stock price in KMW, Inc. is $50, $54, $56, and $48 on four consecutive days of trading. What is the continuously compounded return on the stock over this time frame? A) -3.85 % B) -4.00 % C) -4.08 % D) -4.16 %

Q: Compute Δ for the following call option. The stock is selling for $23.50. The strike price is $25. The possible stock prices at the end of 6 months are $27.25 and $21.75. A) 0.4091 B) 0.6822 C) 0.8433 D) 0.9216

Q: A stock is currently selling for $22.00 per share. Ignoring interest, determine the intrinsic value of a call option should there exist equally probable stock prices of $25.00 and $23.00. A) $0.00 B) $1.00 C) $2.00 D) $3.00

Q: Put-call parity allows a discussion of option pricing relationships without actually pricing an option. Have the class list all the possible pricing relationships they can recall. Add to the list until reasonably complete. Follow up this exercise by listing puts and calls, while asking students to state if certain premiums are possible.

Q: All else being equal, explain why American options are at least as valuable as European options.

Q: The necessary condition for early exercise is that we prefer to receive something sooner rather than later. With a dividend paying call and a non-dividend paying put, what do we receive?

Q: Explain in simple terms why a call option on a non-dividend paying stock should never be exercised early.

Q: Jillo, Inc. stock is selling for $54.70 per share. Calls and puts with a $55.00 strike and 40 days until expiration are selling for $1.65 and $1.23, respectively. Draw a profit and loss graph illustrating the arbitrage.

Q: Using the synthetic long stock strategy, explain the difference in call and put prices.

Q: The price of a non-dividend paying stock is $55 per share. A 6-month, at the money call option is trading for $1.89. If the interest rate is 6.5%, what is the likely price of a European put at the same strike and expiration?A) $0.05B) $0.13C) $0.56D) $0.88

Q: The spot exchange rate in dollars per euro is $1.31. Dollar denominated interest rates are 4.0% and euro denominated interest rates are 3.0%. What is the difference in call and put option prices given a 2-year option and a $1.34 strike price? A) -$0.1041 B) -$0.0652 C) $0.1233 D) $0.1546

Q: Consider the case of an exchange option in which the underlying stock is Eli Lilly and Company with a current price of $56.00 per share. The strike asset is Merck, with a per share price of $52.00. Interest rates are 5% and the 3-month call option is trading for $7.00. What is the price of the put? A) $3.00 B) $4.00 C) $7.00 D) $11.00

Q: Put options with strikes of $70, $75, and $85 have option premiums of $6.00, $8.50, and $11.00, respectively. Using strike price convexity, which option premium, if any, is not possible? A) P (70) B) P (75) C) P (85) D) All are possible

Q: Call options with strikes of $30, $35, and $40 have option premiums of $1.50, $1.70, and $2.00, respectively. Using strike price convexity, which option premium, if any, is not possible? A) C (30) B) C (35) C) C (40) D) All are possible

Q: Which of the following options will NOT be exercised early? A) Put on a dividend paying stock B) Call on a dividend paying stock C) Put on a non-dividend paying stock D) Call on a non-dividend paying stock

Q: The 6-month call and put premiums are $0.114 and $0.098, respectively, with a $0.94 strike. Dollar and euro interest rates are 7.0% and 6.0%, respectively. What spot exchange rate is implied by this data? A) $0.98 dollars per euro B) $1.02 dollars per euro C) $1.05 dollars per euro D) $1.09 dollars per euro

Q: The spot exchange rate of dollars per euro is 0.95. Dollar and euro interest rates are 7.0% and 6.0%, respectively. The price of a $0.93 strike 6-month call option is $0.08. What is the price of the put? A) $0.016 B) $0.032 C) $0.056 D) $0.078

Q: Jillo, Inc. stock is selling for $54.70 per share. Calls and puts with a $55 strike and 40 days until expiration are selling for $1.65 and $1.23, respectively. What potential arbitrage profit exists? A) $0.12 B) $0.24 C) $0.36 D) $0.48

Q: The price of a stock is $52.00. Lacking additional information, what is your forecasted difference between a put option and a call option on this stock? Assume 38 days to expiration and 6.0% interest. A) $0.16 B) $0.32 C) $0.48 D) $0.64

Q: A company is forecasted to pay dividends of $0.90, $1.20, and $1.45 in 3, 6, and 9 months, respectively. Given interest rates of 5.5%, how much dollar impact will dividends have on option prices? (Assume a 9-month option.) A) $3.45 B) $3.90 C) $4.22 D) $4.50

Q: Rankin Corp. common stock is priced at $74.20 per share. The company just paid its $1.10 quarterly dividend. Interest rates are 6.0%. A $70.00 strike European call, maturing in 6 months, sells for $6.50. How much arbitrage profit/loss is made by shorting the European call, which is priced at $2.50? A) $0.12 loss B) $0.12 gain C) $0.36 loss D) $0.36 gain

Q: Jafee Corp. common stock is priced at $36.50 per share. The company just paid its $0.50 quarterly dividend. Interest rates are 6.0%. A $35.00 strike European call, maturing in 6 months, sells for $3.20. What is the price of a 6-month, $35.00 strike put option? A) $1.20 B) $1.64 C) $2.04 D) $2.38

Q: How does the existence of swaptions add to the possibilities in risk management techniques?

Q: Why do arbitrage profits rarely exist in interest rate swap pricing?

Q: How would a market-maker hedge a swap involving variable price and quantity?

Q: Explain a "diff swap" as it relates to currency swaps.

Q: Under what circumstances would a multinational company elect to enter into a currency swap agreement?

Q: Describe briefly the nature of a swap and its primary component.

Q: An investor enters into a 2-year swap agreement to euros at $1.32 per euro. Soon after the swap is created forward prices rise and the new swap price on a similar swap is $1.45. If dollar denominated interest rates are 4.0% and 4.5% on 1- and 2-year zero coupon government bonds, respectively, what is the gain to be made from unwrapping the original swap agreement?A) $0.24B) $0.45C) $0.65D) $0.82

Q: The forward prices on a barrel of crude oil are $112 and $118 in years one and two, respectively. The interest rates on zero coupon government bonds are 3.0% and 3.5% in years one and two, respectively. What is the likely 2-year swap price on a barrel of crude oil? A) $112.00 B) $116.60 C) $118.00 D) $120.50

Q: An investor enters into a 2-year swap agreement to purchase crude oil at $105.65 per barrel. Soon after the swap is created forward prices rise and the new swap price on a similar swap is $108.32. If interest rates are 3.0% per year, what is the gain to be made from unwrapping the original swap agreement? A) $2.67 B) $5.11 C) $5.34 D) $5.67

Q: A portfolio manager enters into a total return swap. She swaps 50% of her $50 million index based portfolio for 4.5% yield bonds. If the annualized total return on the index is 2.5%, what net cash flow will the manager experience under the swap agreement? A) + $250,000 B) -$250,000 C) + $500,000 D) -$500,000

Q: Your company can get yen loans for 2.0%. Dollar rates on the same loans are 4.5%. The spot yen per dollar exchange rate is 104. The forward rates for years 1 thru 4 are, 101.51, 99.08, 96.71, and 94.40, respectively. What is the present value of the market-maker's net cash flow if spot rates are 102 instead? A) $188.59 B) $206.43 C) $219.96 D) $242.06

Q: Your company can get yen loans for 2.0%. Dollar rates on the same loans are 4.5%. The spot yen per dollar exchange rate is 104. The forward rates for years 1 thru 4 are, 101.51, 99.08, 96.71, and 94.40, respectively. What is the dollar value of a 4-year 1 million yen loan? A) $9,615.33 B) $10,422.46 C) $11,618.04 D) $13,527.89

Q: Euro dollar futures prices with maturities of 3, 6, and 9 months are 89.04, 88.75, and 88.55, respectively. What is the annualized swap rate on 9-month securities? A) 8.55% B) 9.68% C) 11.34% D) 13.24%

Q: IBM and AT&T decide to swap $1 million loans. IBM currently pays 9.0% fixed and AT&T pays 8.5% on a LIBOR + 0.5% loan. What is the net cash flow for IBM if they swap their fixed loan for a LIBOR + 0.5% loan and LIBOR rises to 8.5%? A) -$50,000 B) $50,000 C) -$90,000 D) 0

Q: Assume the net swap payment is $.50 on a reverse transaction involving a 3-year oat swap. What is the market value of the swap given interest rates on zero coupon treasury bonds are 5.2%, 5.6%, and 6.0% for 1, 2, and 3 years, respectively? A) $0.96 B) $1.10 C) $1.25 D) $1.34