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.
True
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