If you create a butterfly spread using 3 put options, the profit will be different from the butterfly spread using 3 call options with the same strike prices.
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False
A European call and a European put with the same underlying/expiration/strike price have the same implied volatility.
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False
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.
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False
Higher risk-free rate increases the value of put options.
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False
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 $6.99, the put with strike price of $50 is $11.06, and the put with strike price of $60 is $21.56. If the stock price becomes $62 at the option expiration, what will be the total profit from the butterfly spread?
The price of an American call on a non-dividend-paying stock is $4.3. The stock price is $42.65, strike price is $41, 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?
Currently, a stock price is $52. 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 4% per annum with continuous compounding. What is the value of a 1-year European put option with a strike price of $50?
Suppose that put options on a stock with strike prices $45 and $55 cost $2 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?
Currently the index is standing at 1,053. 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 $35.49. What is the value of a 6-month European call option on the index with the same strike price?
A call option expiring in 62 trading days has a market price of $11. The current stock price is $60, 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%
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?
A call option on a non-dividend-paying stock has a market price of $5.80. 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%
Suppose the current stock price is $50. At the end of 6 months it will be either $58 or $44. 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%.
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?
$664.81
$778.50
$639.26
$659.92
If the stock price is less than the strike price, one should exercises the American put option.
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False
It's never optimal to early exercise an American put, if the underlying pays dividend.
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False