Finance 477 Final

6.95

Assume European futures call and put options with following parameter values: T = 0.5; r = 0.05; F0=100; K=102. If the call option is worth $5, what is the value of the put?

4.61

Consider a European call option on a non-dividend-paying stock where the stock price is $40, the strike price is $40, the risk-free rate is 4% per annum, the volatility is 30% per annum, and the time to maturity is six months. What is the value of this option according to a one-step binomial model of Cox, Ross and Rubinstein?

0.23

Consider a European put option on a currency. The exchange rate is $1.15 per unit of the foreign currency, the strike price is $1.25, the time to maturity is one year, the domestic risk-free rate is 0% per annum, and the foreign risk-free rate is 5% per annum. The volatility of the exchange rate is 0.25. What is the value of this put option according to a one-step binomial tree? Please provide your answer in the unit of dollar, to the nearest cent, but without the dollar sign (for example, if your answer is $1.02, write 1.02).

2438.3

Suppose that the current Bitcoin futures price is $30,000, and the risk free rate is 5% per annum (with continuous compounding). What is the lower bound of the value of a six-month put option on one Bitcoin futures contract with a strike price of $32,500?

4

Which of the following statements about a straddle is NOT true? 1. A straddle is more expensive than a comparable strangle (assuming that the underlying asset and the maturity are the same). 2. The payoff of a straddle is generally higher than the payoff a comparable strangle (assuming that the underlying asset and the maturity are the same). 3. A long straddle should be used if you believe that the volatility of the underlying asset is underestimated by the market. 4. A long straddle generates the highest profit when the price of underlying asset stays close to the strike price..

Answer 4

Which of the following statements about an option is Incorrect? 1. A call option on a stock cannot be more valuable than the stock itself. 2. A price of a put option should not be higher than the strike price. 3. An American call option on a non-dividend-paying stock should not be exercised before maturity. 4. An American put option on a non-dividend-paying stock should not be exercised before maturity.

3

Which of the following statements about embedded options NOT true? 1. Equity can be viewed as a call option on the firm value. 2. Risky debt can be viewed as risk-free debt minus a put option. 3. Risky debt can be viewed as risk-free debt plus a put option. 4. A convertible bond can be viewed as a straight bond plus a call option.

Volatility of the underlying asset price

Which of the following variables is positively related to the values of both puts and calls? 1. Interest rate 2. Strike price 3. Volatility of the underlying asset price 4. Price of the underlying asset

16

A 1-week European at-the-money call option on the Apple stock is trading at $16. An investor buys an Apple stock and shorts the call at their market prices. What is this investor's maximum gain at the option maturity? Please provide your answer in unit of dollars without the dollar sign.

12.35

A 1-week European call option on the Apple stock is trading at $4. A 1-week European put option with the same strike price is trading at $4.35. An investor longs a strap using these two options. What is the maximum loss for this investor at the option maturity? Please provide your answer in unit of dollars without the dollar sign.

true

A Call cannot be worth more than the underlying stock True or False

1.75

A call option with a strike price of $10 is trading at a price of $1.75. The price of the underlying asset is $9.5. What is the time value of this option? (Your answer should be in the unit of dollar, to the nearest cent, and without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

101.9

A foreign currency is currently worth $1.5 per unit. The domestic and foreign risk-free rates are 5% and 9% per annum (continuously compounded), respectively. The volatility of the exchange rate is 15% per annum. What is the value of a 12-month European call option on 1000 units of the foreign currency with a strike price of $1.40 according to the BSM model? (please express your answer in dollar, to the nearest cent, without the dollar sign. Feel free to check your answer using RMFI before your submit.)

6.79

A futures price is currently 40 dollars. It is expected to move up to 44 dollars or down to 34 dollars in the next six months. The continuously-compounded risk-free interest rate is 6% per annum. What is the value of a six-month European call on the futures contract with a strike price of 33 dollars? Please note that the option will be in the money in both states. Please provide your answer in unit of dollars without the dollar sign (rounded to the nearest cent). For example, if your answer is $1.02, write 1.02.

1.25

A put option with a strike price of $10 is trading at a price of $1.75. The price of the underlying asset is $9.5. What is the time value of this option? (Your answer should be in the unit of dollar, to the nearest cent, and without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

16.9

A stock index is currently 300, the dividend yield on the index is 3% per annum (continuously compounded), and the risk free interest rate is 8% per annum (continuously compounded). What is the lower bound for the price of a 6-month European call option on the index with a strike price of 290? (please express your answer in dollar, to the nearest cent, without the dollar sign.)

1.08

A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or decrease by 10%. No dividend payment is expected during these two periods. The risk-free interest rate is 5% per annum. If you use a two-step tree to do the valuation, what, to the nearest cent, is the value of a European call option with a strike price of $32 that expires in four months? (Your answer should be in the unit of dollar, but without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

2.59

A stock price is currently $30. During each two-month period for the next four months it is expected to increase by 8% or decrease by 10%. No dividend payment is expected during these two periods. The risk-free interest rate is 5% per annum. If you use a two-step tree to do the valuation, what, to the nearest cent, is the value of a European put option with a strike price of $32 that expires in four months?

True

An European put cannot be worth more than the PV of the strike price True or False

195

An at-the-money call option on Amazon costs $100, an at-the-money put option on Amazon with the same strike price costs $95. What is the maximum loss of a long straddle strategy?

-950

An investor buys a Bitcoin at the price of $57,000. At the same time, he sells a one-month call option on a Bitcoin with a strike price of 58,000 for $1200, and buys a one-month put option on a Bitcoin with a strike price $56,000 at $1150. If the Bitcoin price in month turns out to be $50,000. What is the profit from this strategy?

550

An investor buys a Bitcoin at the price of $57,000. At the same time, he sells a one-month call option on a Bitcoin with a strike price of 58,000 for $1200, and buys a one-month put option on a Bitcoin with a strike price $56,000 at $1150. If the Bitcoin price in month turns out to be $57,500. What is the profit from this strategy?

1050

An investor buys a Bitcoin at the price of $57,000. At the same time, he sells a one-month call option on a Bitcoin with a strike price of 58,000 for $1200, and buys a one-month put option on a Bitcoin with a strike price $56,000 at $1150. If the Bitcoin price in month turns out to be $60,000. What is the profit from this strategy?

965

An investor creates a covered call position by purchasing 100 shares of the Tesla stock at a price of $1050 per share and selling 100 call options on the Tesla stock with a strike price $1050 per share. The premium of the option is $85 per share. At which stock price at the maturity of the option will the investor break even? Please provide your answer in unit of dollars (without the dollar sign), rounded to the nearest cent.

3500

An investor implements a collar strategy by purchasing 100 shares of the Tesla stock at a price of $1040 per share, selling 100 call options on the Tesla stock with a strike price $1080 per share, and buying 100 put option on the Tesla with a strike price of $1000. The premium of each call option is $85 and the premium of each put option is $80. If stock price at the maturity of the option turns out to be $1070. What is the investors' profit? Please provide your answer in unit of dollars (without the dollar sign), rounded to the nearest cent.

0.21

Consider a European put option on a currency. The exchange rate is $1.15 per unit of the foreign currency, the strike price is $1.25, the time to maturity is one year, the domestic risk-free rate is 0% per annum, and the foreign risk-free rate is 5% per annum. The volatility of the exchange rate is 0.25. What is the value of this put option according to the Black-Scholes-Merton model? Please provide your answer in the unit of dollar, to the nearest cent, but without the dollar sign (for example, if your answer is $1.02, write 1.02). Please provide your answer in the unit of dollar, to the nearest cent, but without the dollar sign (for example, if your answer is $1.02, write 1.02).

98727

Consider a call option to buy 100,000 shares with the following parameters: S0=10 K=9.5 σ=0.2 r=0.05 T=0.5 Please determine the value this option Monte Carlo simulation with 10000 trials.

5.07

Consider a six-month European call option on a non-dividend-paying stock. The stock price is $30, the strike price is $29, and the continuously compounded risk-free interest rate is 6% per annum. The volatility of the stock price is 50% per annum. What is price of the call option according to the Black-Schole-Merton model? Please provide you answer in the unit of dollar, to the nearest cent, but without the dollar sign (for example, if your answer is $1.02, write 1.02).

2.6

Consider a six-month European call option on a stock. The stock price is $30, the strike price is $29, and the continuously compounded risk-free interest rate is 6% per annum for all maturities. There is a dividend of $3 and the ex-dividend date is in three months. The volatility of the stock price is 40% per annum. What is price of the call option? Please provide your answer in unit of dollars without the dollar sign (rounded to the nearest cent). For example, if your answer is $1.02, write 1.02. Hint: Please use the BSM formula to value this option, accounting for the effect of dividend.

129.17

Consider a six-month European call option on an index. The current index value is 2030, the strike price is 2090, the dividend yield is 2% per annum, and the continuously compounded risk-free interest rate is 6% per annum. The volatility of the index is 20% per annum. What is price of the option according to a one-step binomial tree? Please provide your answer in the unit of dollar, to the nearest cent, but without the dollar sign (for example, if your answer is $1.02, write 1.02).

314.16

Consider a six-month European call option on an index. The current index value is 4130, the strike price is 4150, the dividend yield is 2% per annum, and the continuously compounded risk-free interest rate is 6% per annum. The volatility of the index is 20% per annum. What is price of the option according to a one-step binomial tree?

260.82

Consider a six-month European call option on an index. The current index value is 4130, the strike price is 4150, the dividend yield is 2% per annum, and the continuously compounded risk-free interest rate is 6% per annum. The volatility of the index is 20% per annum. What is price of the option according to the BSM model?

0.46

Consider a two-step binomial tree in which the risk-neutral probability that price of the underlying asset moves upward at each node is p=0.65. What is the risk-neutral probability that the underlying asset price reaches the middle node at the end of the second period?

20

Consider an American put option on a stock expiring in 9 months. The annualized volatility of the stock, which pays no dividends, is 0.3. The risk-free rate is 10% per annum (continuously-compounded). The strike price of the option is $120, and the current stock price is 100. What is the value of this American option based on a one-step Cox-Ross-Rubinstein model?

False

If the strike price, time to maturity, underlying asset, and option type (call vs. put) are the same, an European-style Asian option is more valuable than an European option. True or False

10

On the day before Facebook released its first quarterly report, investor B bought 100 European call options on the Facebook stock with strike price of $200 per share, and bought 100 European put options on the stock with a strike price $200 per share. Both options had a time to maturity of two days. The premium for the first option was $5 per share, and the premium for the second option was $4.9 per share. Two days later, the stock was trading at $190 per share. What was the profit earned by this investor over these two days?

-1050

On the day before Facebook released its first quarterly report, investor C bought 100 European call options on the Facebook stock with strike price of $190 per share, and sold 100 European call options on the stock with a strike price $210 per share. Both options had a time to maturity of two days. The premium for the first option was $15 per share, and the premium for the second option was $4.5 per share. Two days later, the stock was trading at $190 per share. What was the profit earned by this investor over these two days?

-600

On the day before Facebook released its quarterly report, investor A bought 100 shares of the Facebook stock at the price of $200 per share, and sold 100 European call options on the stock expiring in two days. The strike price of the option was $200 per share and the option premium was $4 per share. Two days later, the stock was trading at $190 per share. What was the profit earned by this investor over these two days? Please use a positive number to represent a profit and a negative to represent a loss.

1.64

Suppose that the current futures price is 30 and that it will move either up to 33 or down to 28 over the next month. The risk free rate is 6% per annum (with continuous compounding). Consider a one-month call option on the futures contract with a strike price of 29. What is the price of this option according to a one-step binomial tree model?

1

Suppose you buy a call option on the October gold futures contract with a strike price of $1800 per ounce. Each futures contract represents 100 ounces of gold. What happens if you exercise when the October futures price is $1,860? 1. A cash payoff of $6000 and a long position in one October gold futures contract entered at $1,860 per ounce. 2. A cash payoff of $6000 and a short position in one October gold futures contract entered at $1,860 per ounce.

1

Suppose you buy a put option on an October gold futures contract with a strike price of $1800 per ounce. Each futures contract represents 100 ounces. What happens if you exercise when the October futures price is $1,760? 1. You get a cash payoff of $4000 and a short position in one October gold futures contract entered at $1,760 per ounce.. 2. You get a cash payoff of $-4000 and a short position in one October gold futures contract entered at $1,760 per ounce.. 3. You get a cash payoff of $4000 and a long position in one October gold futures contract entered at $1,760 per ounce.. 4. You get a cash payoff of $-4000 and a long position in one October gold futures contracted entered at $1,760 per ounce.

1.55

The current exchange rate is JPY 80 = CAD 1, the volatility of the exchange rate is 20% per annum. The continuously compounded risk free rate is 6% per annum in Canada and 10% per annum in Japan. What is the value of a five-month European put on CAD 1 with a strike price of JPY 75 computed using the BSM model?

2.97

The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume that the risk-free rate is 10% per annum (continuously compounded). What, to the nearest cent, is the value of a 6-month European put option on the stock with a strike price of $33?

1.58

The current price of a non-dividend-paying stock is $30. Over the next six months it is expected to rise to $36 or fall to $26. Assume that the risk-free rate is 10%. What, to the nearest cent, is the value of a 6-month European call option on the stock with a strike price of $33?

0.44

The current price of a non-dividend-paying stock is $30. Over the next three months it is expected to rise to $36 or fall to $26. Assume that the risk-free rate is 5% per annum (continuously compounded). What is the risk-neutral probability of the stock price moving up to $36? (please write your answer in decimal form with two decimal places.)

1.74

The current price of a non-dividend-paying stock is $30. Over the next three months it is expected to rise to $36 or fall to $26. Assume that the risk-free rate is 5% per annum (continuously compounded). What is the value of a three-month call option with strike price of $32? (please write your answer with two decimal places.)

3.32

The current price of a non-dividend-paying stock is $30. Over the next three months it is expected to rise to $36 or fall to $26. Assume that the risk-free rate is 5% per annum (continuously compounded). What is the value of a three-month put option with strike price of $32? (please write your answer with two decimal places.)

6

The current price of a non-dividend-paying stock is $60. Over the next six months it is expected to rise to $72 or fall to $56. Assume the risk-free rate is 10% per annum (continuously compounded). What, to the nearest cent, is the price of an American put option with a strike price of $66? (Your answer should be in the unit of dollar, but without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

5.23

The current price of a non-dividend-paying stock is $60. Over the next six months it is expected to rise to $72 or fall to $56. Assume the risk-free rate is 10% per annum. What, to the nearest cent, is the price of a European put option with a strike price of $66? (Your answer should be in the unit of dollar, but without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

1.41

The current price of a non-dividend-paying stock is 30. The volatility of the stock is 0.3 per annum. The risk free rate is 0.05 for all maturities. Using the Cox-Ross-Rubinstein binomial tree model with one time step to do the valuation, what is the value of a European call option with a strike price of 32 that expires in 3 months? (Your answer should be in the unit of dollar (up to the precision of cents), but without the dollar sign. For example, if your answer is $1.02, just enter 1.02. Please also think whether your answer will be different if the option is an American option.)

33.75

The current price of a stock $150, and the volatility of the stock is estimated to be 45% per year. What is your estimate of the standard deviation of the stock price change in one quarter?

1.95

The current price of a stock is $19. There is a dividend of $2 to be paid in 9 month. The risk-free rate is 5% per annum. What is the lower bound of the value of a 12-month European put option with a strike price of $20?

41.04

The current price of a stock is 300. The volatility is of the stock price is 50% per annum. There is a dividend of $15 to be paid in 3 months (assuming that the ex-dividend date is the same as the dividend payment date). The continuously compounded risk-free rate is 5% per annum. What is the price of a six-month call option with a strike price of $290 based on the Black-Scholes-Merton model?

690.38

The current price of gold is $1865 per ounce. The volatility of gold price is 20% per annum. The continuously-compounded risk-free rate is 5% per annum. What is the value of a 3-month call option on 10 ounces of gold with a strike price of $1900 according to the BSM model?

3

The current price of the futures contract is $30. A six-month call option on the futures contract with a strike price of $30 is trading at a price of $3. What is the price of a six-month put option on this futures contract with the same strike price? Please provide your answer in unit of dollars without the dollar sign (rounded to the nearest cent). For example, if your answer is $1.02, write 1.02.

4.82

The following information about a call option on a stock is given. What is the value of this call option based on the BSM model? Dividend =0 Time to maturity=0.25 Current stock price =40.75 Strike price=40 Annualized risk-free rate =5% (continuously compounded) Annual volatility=0.5224

-2.5

The price of a European call on a stock with a strike price of $10 is $7. The price of a European call on the same stock with a strike price 15 is $3. The maturities of these two options are the same. An investor creates a bull spread using these two options. If the underlying stock price at the maturity is $11.50. What is the profit earned by this investor? Please provide your answer in dollars without the dollar sign (rounded to the nearest cent).

14

The price of a European call on a stock with a strike price of $10 is $7. The price of a European call on the same stock with a strike price 15 is $3. The maturities of these two options are the same. An investor creates a bull spread using these two options. What is the stock price at the end of the maturity that will make this investor break even? Please provide your answer in dollars without the dollar sign (rounded to the nearest cent).

13

The price of a European call on a stock with a strike price of $10 is $7. The price of a European call on the same stock with a strike price 15 is $4. The maturities of these two options are the same. An investor creates a bull spread using these two options. What stock price at the end of the maturity that will make this investor break even?

Sell the put, short sell the stock but the call and invest any cash surplus in a risk-free bond

The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% per annum and the time to maturity is one year. If the put option is quoted at a price of $3 in the market, how would you arbitrage?

2.09

The price of a European call option on a non-dividend-paying stock with a strike price of $50 is $6. The stock price is $51, the continuously compounded risk-free rate (all maturities) is 6% per annum and the time to maturity is one year. What, to the nearest cent, is the price of a one-year European put option on the stock with a strike price of $50? (Your answer should be in the unit of dollar, but without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

Buy the put, buy the stock, sell the call and borrow 19

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 price of a three-month European put option with a strike price of $20 is also $1? The risk-free rate is 4% per annum. How should you arbitrage?

1.8

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 of a three-month European put option with a strike price of $20? Hint: use the put-call parity.

6.43

The price of a non-dividend-paying stock is $20. The continuously-compounded risk-free interest rate is 5% per annum. What, to the nearest cent, is the lower bound for the price of a two-year European call option on the stock with a strike price of $15? (Your answer should be in the unit of dollar, but without the dollar sign. For example, if your answer is $1.02, just enter 1.02.)

2.79

The price of a stock is $19. The risk-free rate is 4% per annum. A dividend of $2 will be paid out in two months on the ex-dividend date. What is the lower bound of the price of a three-month European put option with a strike price of $20?

2.21

The price of a stock is $19. The risk-free rate is 4% per annum. A dividend of $2 will be paid out in two months on the ex-dividend date. Strike = 20, T=3/12 If the price of the European put is $5. What is the price of the European call?

0

The price of a stock is $19. The risk-free rate is 4% per annum. A dividend of $2 will be paid out in two months on the ex-dividend date. What is the lower bound of the value of a three-month European call option on the stock with a strike price of $20?

True

The price of an at-the-money European call futures option should equal the price of a similar at-the-money European put futures option. True or False

15

The put option on the Alibaba stock with strike prices of $200 trades at $15. An investor buys a share of the stock at the price of $200 and longs the put at the same time. What is the investor's maximum loss at the maturity of the option? Please provide your answer in unit of dollars (without the dollar sign). If the maximum loss is $50, then write 50 (don't write -50 just because it is a loss! A loss of -50 is a gain of 50.)

C

The risk-free rate is 5% and the expected return on a non-dividend-paying stock is 12%. A derivative can be valued by (choose one) HInt: this is a question about the risk-neutral valuation approach. a)Assuming that the expected growth rate for the stock price is 12% and discounting the expected payoff at 12% b) Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 12% c) Assuming that the expected growth rate for the stock price is 5% and discounting the expected payoff at 5% d) Assuming that the expected growth rate for the stock price is 12% and discounting the expected payoff at 5%

False

The risk-neutral valuation method works only if investors are risk-neutral. True or False

0.35

The stock price today is 20. In three months, it can either increase to 22 or drop to 18. The continuously compounded risk-free rate is 12% per annum. What is the risk-neutral probability of the price decreasing to 18? (Write your answer in decimal form with two decimal places.)

The probability that a standard normally distributed random variable has realized value below d1

What is the meaning of N(d1) in the Black-Scholes-Merton option pricing formulas?

5.15

What is the value a European put futures option with the following parameters based on a one-step binomial tree model? T = 0.5 r = 0.05 σ = 0.12 F0=100 K=102

A

Which of the following is NOT true? (a) The time value of an option is never negative. (b) The intrinsic value of an option is never negative. (c) The value of an option is never negative. (d) For an American option, neither the intrinsic value nor the time value is negative.

3

Which of the following set of variables are positively related to the values of call options and negatively related to the values of put options? 1. Risk free rate and dividend. 2. Volatility and strike price. 3. Risk free rate and underlying asset price. 4. Time to maturity and strike price.

2

Which of the following set of variables are positively related to the values of put options and negatively related to the values of call options? 1. Dividend and risk free rate. 2. Dividend and strike price. 3. Strike price and time to maturity. 4. Volatility and time to maturity.

3

Which of the following statement about the delta of an option is Incorrect? 1. Delta measures the sensitivity of the option value with respect to the price of the underlying asset. 2. The delta of a call option is positive and the delta of a put option is negative. 3. The delta of an option is constant over time. 4. A portfolio with a short position in an option and delta units of the underlying asset is locally risk-free.

2

Which of the following statements about VIX is NOT true? 1. VIX usually moves up when the stock market goes down. 2. Other things equal, when VIX goes up, options on the S&P500 index become cheaper. 3. An increases in VIX indicates that investors feel more uncertain about the movement of the stock market. 4. VIX is a forward-looking measure of market volatility.