1. What is a lower bound for the price of a 4-month call option on a non-dividend -paying stock when the stock price is $43.77, the strike price is $36, and the risk-free interest rate is 5% per annum?
2. If the underlying pays no dividend, then the early exercise payoff of an American call option is always smaller than the remaining value of the option.
True
False
3. Currently, a stock price is $53. Over each of the next 2 6-month periods it is expected to go up by 12% or down by 10%. The risk-free rate is 5% per annum with continuous compounding. What is the value of a 1-year European put option with a strike price of $50?
4. One should use straddle, if he thinks there will be a significant stock price move in either direction.
True
False
5. A call with a strike price of $70 costs $7.66. A put with the same strike price and expiration date costs $3.68. If you create a straddle, what is the initial cash flow?
6. Suppose you are creating a butterfly spread using 3 call options with different strike prices. Currently, the call price with strike price of $40 is $20.22, the call with strike price of $50 is $11.29, and the call with strike price of $60 is $5.55. What is the initial cash flow of the butterfly spread strategy?
7. Calculate the price of a 4-month European call option on a dividend-paying stock with a strike price of $30 when the current stock price is $32, the risk-free rate is 6% per annum and the volatility is 40% per annum. A dividend of $1.00 is expected in 2 months. Use Black-Scholes formula.
$3.05
$3.65
$4.32
$5.02
8. Suppose that put options on a stock with strike prices $45 and $55 cost $5 and $8, respectively. Use these options to create a bear spread. At what stock price at maturity will you break even? In other words, at what stock price, will you make $0 profit?
9. Which of the following does not affect the Black-Scholes option prices for a non dividend paying stock?
current stock price
strike price
expected return of stock
volatility of stock
risk-free interest rate
10. A call option expiring in 40 trading days has a market price of $7. The current stock price is $55, the strike price is $50, and the risk-free rate is 3% per annum. Calculate the implied volatility.
33.23%
34.57%
42.62%
46.04%
11. Suppose the current stock price is $50. At the end of 6 months it will be either $58 or $43. The risk-free interest rate is 3% per annum. What is the risk-neutral probability that the stock price will increase in 6 months? Report in percentage such as 55.55%.
12. Higher strike price increases the value of put options.
True
False
13. The price of an American call on a non-dividend-paying stock is $4.25. The stock price is $41.42, strike price is $39, and the expiration date is in 3 months. The risk-free rate is 6%. What is the upper bound for the price of an American put on the same stock with the same strike price and expiration date?
14. Suppose your portfolio mirrors S&P500 index and is valued currently at $1,000,000. The S&P 500 index is currently at 2,000. What action is needed to provide protection against the value of the portfolio falling below $900,000 in 6 months?
Buy 5 6-month S&P500 put option contracts with strike price of 1800.
Buy 5 6-month S&P500 put option contracts with strike price of 1900.
Buy 10 6-month S&P500 put option contracts with strike price of 1800.
Buy 10 6-month S&P500 put option contracts with strike price of 1900.
15. Currently, a stock price is $80. It is known that at the end of 4 months it will be either $70 or $90. The risk-free rate is 6% per annum with continuous compounding. What is the value of a 4-month European put option with a strike price of $80?
16. Currently the index is standing at 1,097. The risk-free rate is 4% per annum and the dividend yield is 1% per annum. A 6-month European put option on the index with a strike price of 1000 is trading at $32.04. What is the value of a 6-month European call option on the index with the same strike price?
17. The price of a non-dividend paying stock is $20.93 and the price of a 3-month European call option on the stock with a strike price of $20 is $7.8. The risk-free rate is 5% per annum. What is the price of a 3-month European put option with a strike price of $20?