1) Currently, a stock price is $51. 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 3% per annum with continuous compounding. What is the value of a 1-year European put option with a strike price of $50?
2) Which strategy benefits from stock price increase but still has some protection against stock price fall?
bull spread
bear spread
butterfly spread
long put
3) Which of the following Greek letter measures the option value sensitivity to time?
Delta
Theta
Vega
Rho
4) One should use butterfly spread, if he thinks there will be a significant stock price move in either direction.
True
False
5) A stock price is currently $70. Over each of the next two three-month periods, it is expected to go up by 8% or down by 6%. The risk-free rate is 4% per annum with continuous compounding. What is the value of a six-month American put option with a strike price of $73?
$5.146
$2.239
$4.036
$2.644
6) Currently, a stock price is $80. It is known that at the end of 4 months it will be either $72 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?
7) Suppose your portfolio's beta is 1.5 and it's valued currently at $400,000. The S&P 500 index is currently at 1000. The riskfree rate is 12% per annum and the dividend yield on both the index and the portfolio is 4%. What action is needed to provide protection against the value of the portfolio falling below $330,000 in 3 months?
Buy 4 3-month put option contracts on index with strike price of 850.
Short 9 3-month call option contracts on index with strike price of 940.
Buy 6 3-month put option contracts on index with strike price of 890.
Short 10 3-month call option contracts on index with strike price of 960.
8) Currently the stock index stands at 1,000 with a volatility of 25% per annum. The risk-free rate is 8% and the dividend yield on the index is 2%. What is the value of a six-month American put option on the index with a strike price of 1,000? Use a 10-step binomial tree.
$86.75
$81.73
$57.28
$73.30
9) The price of a non-dividend paying stock is $20.1 and the price of a 3-month European call option on the stock with a strike price of $20 is $1.59. The risk-free rate is 6% per annum. What is the price of a 3-month European put option with a strike price of $20?
10) A call option expiring in 52 trading days has a market price of $4. The current stock price is $50, the strike price is $50, and the risk-free rate is 0.03% per annum. Calculate the implied volatility.
34.48%
39.23%
44.20%
48.20%
11) A stock price is currently $25. At the end of 3 months, it will be either $30 or $20. The risk-free rate is 10% per annum with continuous compounding. Suppose S is the stock price at the end of 3 months. What is the today's value of a derivative that pays S2 in 3 months?
$639.26
$659.92
$664.81
$778.50
12) 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 $2.00 is expected in 2 months. Use Black-Scholes formula.
$3.05
$3.65
$4.32
$5.02
13) A 1-month European call option on a non-dividend-paying stock is currently selling for $2.50. The stock price is $50, the strike price is $47, and the risk-free rate is 6%. What strategy results in an arbitrage profit?
Short call option, short stock, lend $49.50 for 1 month.
Buy call option, short stock, lend $45.50 for 1 month.
Buy call option, buy stock, borrow $49.50 for 1 month.
Short call option, buy stock, borrow $45.50 for 1 month.
14) Suppose you are creating a butterfly spread using 3 put options with different strike prices. Currently, the put price with strike price of $40 is $5.93, the put with strike price of $50 is $12.87, and the put with strike price of $60 is $21.18. If the stock price becomes $64 at the option expiration, what will be the total profit from the butterfly spread?
15) What is the index of the implied volatility of 30-day options on S&P 500 called?
LIBOR
SPX
ED
VIX
16) A call option on a non-dividend-paying stock has a market price of $5.70. The stock price is $20, the strike price is $15, the time to maturity is 6 months, and the risk-free rate is 5% per annum. What is the implied volatility?
36.02%
40.13%
43.78%
47.15%
17) The price of an American call on a non-dividend-paying stock is $4.77. The stock price is $41.3, 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?
18) Higher volatility increases the value of put options.
True
False
19) The American option always has a higher value than a European option, if all other factors are the same.
True
False
20) Put-call parity implies the put option and the call option with the same underlyng, strike price and expiration have the same price.
True
False
21) Currently the index is standing at 1,067. 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 $47.94. What is the value of a 6-month European call option on the index with the same strike price?
22) In binomial pricing, the length of 1 step is equal to the time to expiration.
True
False
23) Suppose that put options on a stock with strike prices $45 and $55 cost $5 and $9, 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?
24) It's never optimal to early exercise an American call, if the underlying pays dividend.
True
False
25) Suppose the current stock price is $50. At the end of 6 months it will be either $59 or $46. The risk-free interest rate is 8% per annum. What is the risk-neutral probability that the stock price will increase in 6 months? Report in percentage such as 55.55%.