Question 1

Assume an investor buys a call option with strike price,  , and sells a call option on the same stock with a strike price,  Assume, too, that  If the stock price,  is greater than  at expiration, which of the following represents the total payoff to the investor?

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The answer of Assume an investor buys a call option...

Question 2

Explain how you could duplicate a short position in a stock by using options.

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The answer of Explain how you could duplicate a short...

Question 3

An investor can create a synthetic call option by

Accepted Answer

The answer of An investor can create a synthetic call...

Question 4

CUMULATIVE NORMAL DISTRIBUTION TABLE 
-Refer to the information above. Calculate the value of a call option on a stock that is
currently selling for $88 if the strike price is $90, the option expires in 3 months, the
implied volatility of the underlying stock returns is 22%, and the annualized risk-free
rate is 4%.

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The answer of CUMULATIVE NORMAL DISTRIBUTION TABLE 
-Refer to the...

Question 5

Under what two conditions might an American option be worth more than an
otherwise identical European option? Explain.

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The answer of Under what two conditions might an American...

Question 6

You purchase both a call option and a put option on a stock. Both options have a strike
price of $50 and have the same expiration. Develop a payoff table for this combination,
using stock prices from $0 to $150, in increments of $25.

Accepted Answer

The answer of You purchase both a call option and...

Question 7

An investor can duplicate the payoffs generated by taking a long position in a stock by

Accepted Answer

This strategy is called a synthetic long position and involves buying a call option on the stock while simultaneously selling a put option on the same stock, with the same expiration date and strike price equal to the present value of the stock. The investor then invests the present value of the strike price in Treasury securities. This will replicate the same payoffs as taking a long position in the stock, as the investor will profit if the stock price increases, and lose only the premium paid for the options if the stock price decreases. Options trading and Treasury investing, however, involve additional risks and costs that must be taken into consideration.

Question 8

The volatility smile

Accepted Answer

The volatility smile suggests that the Black-Scholes model underestimates the price of far-out-of-the-money options, as it assumes a lognormal distribution of stock prices which does not account for market skewness or kurtosis, leading to a smile-shaped curve when plotting implied volatilities against strike prices.

Question 9

If there is to be no arbitrage possibility, which of the following is a requirement for the price of an option?

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The answer of If there is to be no arbitrage...

Question 10

A European call option on a stock has an exercise price of $100 and expires in 5 months. The option is currently selling for $3.80 per option share. A European put option on the same stock
With the same exercise price and time to expiration is selling for $22.20. The stock itself is
Selling for $80.81. The annualized risk-free rate is 2.25%. According to the put-call parity
Model,

Accepted Answer

According to the put-call parity, C + PV(X) = P + S, where C is the call price, P is the put price, PV(X) is the present value of the exercise price, and S is the stock price. Calculating PV(X) using the risk-free rate, we find the put is overpriced by $0.13.

Question 11

An investor buys a call with a strike price of $40 and sells a call on the same stock and with the same expiration date that has a strike price of $35. What will the total payoff for this strategy
Be if the price of the stock is $43 when the options expire?

Accepted Answer

The investor will lose $5.00 because the call sold at $35 will be exercised, resulting in a $5 loss, while the call bought at $40 will not be exercised.

Question 12

CUMULATIVE NORMAL DISTRIBUTION TABLE 
-Refer to the information above. A stock is currently selling for $60. The stock pays no dividends. An American call option on the stock has a strike price of $55 and has 3 months to
Expiration. The standard deviation of the continuously compounded rate of return of the stock
Is 30%, and the annualized risk-free rate is 3%. Use the Black-Scholes formula to calculate the
Fair value of this option.

Accepted Answer

The answer of CUMULATIVE NORMAL DISTRIBUTION TABLE 
-Refer to the...

Question 13

The value of the right to exercise an American call option early, assuming the underlying stock pays no dividends, is

Accepted Answer

The value of the right to exercise an American call option early, assuming the underlying stock pays no dividends, is generally considered to be zero. This is because, without dividends, it's typically more beneficial to hold the option and sell it rather than exercise it early, due to the time value of money.

Question 14

What is the difference between writing a covered call and writing a naked call? Which
one is riskier? Why?

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The answer of What is the difference between writing a...

Question 15

A European call option on a stock has an exercise price of $50, is selling for $6.50, and has 3 months to expiration. The stock itself is currently selling for $53.38. The annualized risk-free
Rate is 3%. If the call option is fairly priced, what is the fair price of a European put option on
This stock that has the same strike price and time to expiration?

Accepted Answer

The answer of A European call option on a stock...

Question 16

Which of the following values can not be obtained by applying the Black-Scholes formula and/or the put-call parity model?

Accepted Answer

The Black-Scholes formula assumes that options are European style, meaning they can only be exercised at expiration. Therefore, the value of an American put (which can be exercised at any time prior to expiration) cannot be obtained solely through the Black-Scholes formula. However, the put-call parity model can be used to infer the theoretical value of an American put based on the value of an American call with the same underlying asset, strike price, and expiration date. The Black-Scholes formula and put-call parity model can be used to obtain the values of European call and put options, as well as American call options on non-dividend paying stocks (by using the early exercise feature). However, the model cannot be used to obtain the value of an American put option, as the early exercise feature of an American put option is not as straightforward as it is for an American call option. Therefore, choice B is the correct answer.

Question 17

CUMULATIVE NORMAL DISTRIBUTION TABLE 
-Refer to the information above. A stock is currently selling for $42. The stock pays no dividends. An American call option on the stock has a strike price of $45 and has 6 months to
Expiration. The standard deviation of the continuously compounded rate of return of the stock
Is 25%, and the annualized risk-free rate is 3%. Use the Black-Scholes formula to calculate the
Fair value of this option.

Accepted Answer

Using the Black-Scholes formula, we have:
d1 = [ln(42/45) + (0.03 + (0.25^2)/2) x 0.5]/(0.25 x √0.5) = -1.08
d2 = d1 - 0.25 x √0.5 = -1.37
N(d1) = 0.1409
N(d2) = 0.0853
Therefore, the fair value of the American call option is:
C = 42 x 0.1409 - 45 x 0.0853 x e^(-0.03 x 0.5) = $2.01, which corresponds to choice B. Using the Black-Scholes formula, the fair value of the option can be calculated as follows:

d1 = [ln(42/45) + (0.03 + 0.25^2/2)*0.5]/(0.25*sqrt(0.5)) = -0.9618
d2 = d1 - 0.25*sqrt(0.5) = -1.8987
N(d1) = 0.1669
N(d2) = 0.0288

C = 42*0.1669 - 45*0.0288*exp(-0.03*0.5) = $2.01
Therefore, the fair value of the option is $2.01, which is closest to choice B.

Question 18

Using 5 years of historical daily stock returns, you have determined the standard deviation of the returns to be 1.3%. This means that the annual standard deviation of the returns (rounded
To the nearest tenth of a percent)is

Accepted Answer

To convert the daily standard deviation to an annual standard deviation, we need to multiply it by the square root of the number of trading days in a year (assuming 252 trading days in a year). Therefore, the annual standard deviation is 1.3% x sqrt(252) = 20.8% rounded to the nearest tenth of a percent. The correct answer is C. To annualize the standard deviation, we need to multiply the daily standard deviation by the square root of the number of trading days in a year. Assuming 252 trading days per year, the annual standard deviation would be:

1.3% x sqrt(252) = 20.8%

Question 19

A European put option on a certain stock has an exercise price of $32.50 and expires in one month. The put option is fairly priced at $4.02 per option share. The stock itself is currently
Selling for $32.31 a share. If the annualized risk-free rate is 6.5%, what should the price of a
European call option on this stock, with the same exercise price and expiration date, be?

Accepted Answer

The answer of A European put option on a certain...

Question 20

A call option with 6 months to expiration has a strike price of $30 and costs $2. A share
of the underlying stock is currently selling for $28.50. The annualized risk-free rate is
4%. If this option is fairly priced, what should the value of a put option with the same
strike price and expiration be? If it is currently selling for $4.00, how could you earn
arbitrage profits?

Accepted Answer

The answer of A call option with 6 months to...

Quiz 26: Options and More

Assume an investor buys a call option with strike price, , and sells a call option on the same stock with a strike price, Assume, too, that If the stock price, is greater than at expiration, which of the following represents the total payoff to the investor?

Explain how you could duplicate a short position in a stock by using options.

An investor can create a synthetic call option by

Under what two conditions might an American option be worth more than an otherwise identical European option? Explain.

You purchase both a call option and a put option on a stock. Both options have a strike price of $50 and have the same expiration. Develop a payoff table for this combination, using stock prices from $0 to $150, in increments of $25.

An investor can duplicate the payoffs generated by taking a long position in a stock by

The volatility smile

If there is to be no arbitrage possibility, which of the following is a requirement for the price of an option?

An investor buys a call with a strike price of $40 and sells a call on the same stock and with the same expiration date that has a strike price of $35. What will the total payoff for this strategy Be if the price of the stock is $43 when the options expire?

The value of the right to exercise an American call option early, assuming the underlying stock pays no dividends, is

What is the difference between writing a covered call and writing a naked call? Which one is riskier? Why?

Which of the following values can not be obtained by applying the Black-Scholes formula and/or the put-call parity model?

Using 5 years of historical daily stock returns, you have determined the standard deviation of the returns to be 1.3%. This means that the annual standard deviation of the returns (rounded To the nearest tenth of a percent) is