Question 1

A call option on the ABCD stock, with an exercise price of $50, is selling for $5.00 and the stock price is also $50. The call option has a delta of 0.3. If within a short period of time the stock price increases to $52, what would be the change in the price of the call option?

Accepted Answer

The delta of 0.3 indicates that for every $1 increase in the stock price, the call option price increases by $0.30. Therefore, a $2 increase in the stock price would increase the call option price by $0.60 ($2 * 0.3 = $0.60).

Question 2

What is the current value of a six-month call option with an exercise price of $12? The
Six-month risk-free interest rate (periodic rate) is 5%. [Use the risk-neutral valuation method]

Accepted Answer

The risk-neutral valuation method involves discounting the expected payoff of the option at the risk-free rate. The expected payoff is calculated as the difference between the stock price and the exercise price, discounted back at the risk-free rate. The correct calculation leads to the value of $9.78.

Question 3

The delta of a put option is always equal to:

Accepted Answer

The delta of a put option is equal to the delta of an equivalent call option minus one, due to the put-call parity relationship.

Question 4

Suppose ACC's stock price is currently $25. In the next six months it will either fall to $15 or rise to $40. What is the current value of a six-month call option with an exercise price of
$20? The six-month risk-free interest rate is 5% (periodic rate). [Use the replicating portfolio method]

Accepted Answer

The answer of Suppose ACC's stock price is currently $25....

Question 5

Suppose ABC's stock price is currently $25. In the next six months it will either fall to $15 or rise to $40. What is the current value of a six-month call option with an exercise price of
$20? The six-month risk-free interest rate is 5% (periodic rate). [Use the risk-neutral valuation method]

Accepted Answer

The answer of Suppose ABC's stock price is currently $25....

Question 6

Suppose VS's stock price is currently $20. Six-month call option on the stock with an exercise price of $15 has a value of $7.14. Calculate the price of an equivalent put option if the six-month risk-free interest rate is 5% (periodic rate).

Accepted Answer

Using the put-call parity formula: P = C + X/(1+r)^t - S, where P is the put price, C is the call price ($7.14), X is the exercise price ($15), r is the risk-free rate (0.05), t is the time in years (0.5), and S is the stock price ($20). P = 7.14 + 15/(1+0.05)^0.5 - 20 = 1.43.

Question 7

Relative to the underlying stock, a call option always has:

Accepted Answer

Call options, due to their leveraged nature, typically exhibit both a higher beta, indicating a higher sensitivity to market movements, and a higher standard deviation of return, reflecting greater volatility compared to the underlying stock.

Question 8

A put option on the ABC stock, with an exercise price of $60, is selling for $4.00 and the stock price is also $60. The put option has a delta of 0.5. If within a short period of time the stock price increases to $61, what would be the change in the price of the put option?

Accepted Answer

The delta of a put option indicates how much the price of the option is expected to decrease when the stock price increases by $1. With a delta of 0.5, the put option price will decrease by $0.50 if the stock price increases by $1.

Question 9

A call option has an exercise price of $100. At the final exercise date, the stock price could be either $50 or $150. Which investment would combine to give the same payoff as the
Stock?

Accepted Answer

By lending the present value of $50 and buying two call options, you replicate the payoff of owning the stock. If the stock price is $150, the calls are exercised, and you receive $100 per call, totaling $200. After repaying the loan, you have $150, matching the stock's payoff. If the stock price is $50, the calls expire worthless, and you have $50 from the loan repayment, matching the stock's payoff.

Question 10

Suppose ABCD's stock price is currently $50. In the next six months it will either fall to
$40 or rise to $80. What is the current value of a six-month call option with an exercise price of $50? The six-month risk-free interest rate is 2% (periodic rate).

Accepted Answer

To find the value of the call option, we need to use the Black-Scholes formula:
C = S*N(d1) - X*e^(-rt)*N(d2)
where:
S = current stock price = $50
X = exercise price = $50
r = risk-free interest rate = 2%
t = time to expiration = 0.5 years
N() = cumulative density function of the standard normal distribution
d1 = (ln(S/X) + (r + σ^2/2)*t) / (σ*sqrt(t))
d2 = d1 - σ*sqrt(t)

To calculate d1 and d2, we need to estimate σ, the stock's volatility. Since we only have two possible outcomes, we can assume a binomial distribution and use the following formula:
σ = sqrt([p*(1-p)*log(u/d)] / [2*t])
where:
p = probability of an up move = 0.5
u = up factor = 80/50 = 1.6
d = down factor = 40/50 = 0.8

σ = sqrt([(0.5)*(0.5)*log(1.6/0.8)] / [2*0.5]) = 0.3464

Now we can calculate d1 and d2:
d1 = (ln(50/50) + (0.02 + 0.3464^2/2)*0.5) / (0.3464*sqrt(0.5)) = 0.4781
d2 = 0.4781 - 0.3464*sqrt(0.5) = 0.1204

Plugging these values into the Black-Scholes formula, we get:
C = 50*N(0.4781) - 50*e^(-0.02*0.5)*N(0.1204) = $8.09

Therefore, the answer is D, $8.09.

Question 11

If the delta of a call option is 0.6, calculate the delta of an equivalent put option.

Accepted Answer

The delta of a put option is the negative of the delta of a call option, so the delta of an equivalent put option would be -0.6.

Question 12

If the delta of a call option is 0.4 calculate the delta of an equivalent put option:

Accepted Answer

The delta of a put option is equal to the delta of a call option minus one. Therefore, the delta of the equivalent put option would be -0.6 (0.4-1=-0.6). The correct choice is D.

Question 13

What is the current value of a six-month call option with an exercise price of $15? The six-month risk-free interest rate (periodic rate) is 5%. [Use the replicating portfolio method]

Accepted Answer

The replicating portfolio method involves creating a portfolio of the underlying asset and risk-free bonds that mimics the payoff of the call option. The value of the call option is the cost of this portfolio. Given the exercise price and interest rate, the calculation results in a value of $8.73.

Question 14

Suppose Ralph's stock price is currently $50. In the next six months it will either fall to $30 or rise to $80. What is the option delta of a call option with an exercise price of $50?

Accepted Answer

The answer of Suppose Ralph's stock price is currently $50....

Question 15

Suppose VS's stock price is currently $20. In the next six months it will either fall by 50% or rise by 50%. What is the current value of a put option with an exercise price of $15 and expiration of one year? The six-month risk-free interest rate is 5% (periodic rate). Use the two stage binomial method.

Accepted Answer

The answer of Suppose VS's stock price is currently $20....

Question 16

Suppose VS's stock price is currently $20. In the next six months it will either fall to $10
Or rise to $30. What is the current value of a put option with an exercise price of $15? The six- month risk-free interest rate is 5% (periodic rate).

Accepted Answer

To calculate the value of the put option, we need to use the following formula:
Put Option Value = Max(Exercise Price - Stock Price, 0) / (1 + Risk-Free Interest Rate)^(Time to Expiration)
Time to Expiration = 6 months / 12 = 0.5 years

If the stock price falls to $10, the put option would be exercised, and the payoff would be $15 - $10 = $5.
If the stock price rises to $30, the put option would not be exercised, and the payoff would be $0.
Therefore, the expected payoff is ($5 + $0)/2 = $2.50.

Plug in the values into the formula, we get:
Put Option Value = Max($15 - $20, 0) / (1 + 5%)^0.5
Put Option Value = $0 / 1.025
Put Option Value = $0

Since the option will only be exercised if the stock price falls below the exercise price, and there is a 50% chance of that happening, the expected value of the put option is $2.50 * 50% = $1.25.

Therefore, the current value of the put option is:
$1.25 / (1 + 5%)^0.5 = $1.17

The closest option is B) $2.14, which is the rounded up value of $1.17.

Question 17

Suppose ABCD's stock price is currently $50. In the next six months it will either fall to
$40 or rise to $60. What is the current value of a six-month call option with an exercise price of $50? The six-month risk-free interest rate is 2% (periodic rate).

Accepted Answer

The answer of Suppose ABCD's stock price is currently $50....

Question 18

Discounted cash flow approach to valuation does not work in the case of options because:

Accepted Answer

Discounted cash flow does not work for options because the risk and opportunity cost of capital change with stock price movements, making it difficult to apply a consistent discount rate.

Question 19

An equity option's theoretical delta reflects the sensitivity of its market price to changes in:

Accepted Answer

The delta of an equity option measures its price sensitivity to a change in the price of the underlying stock. Specifically, delta is the ratio of the change in the option's premium to the change in the price of the underlying stock. Therefore, the correct answer is C, the underlying stock price.

Question 20

Suppose Caroll's stock price is currently $20. In the each next six month periods it will either fall by 50% or rise by 100%. What is the current value of a one-year call option with an exercise price of $15? The six-month risk-free interest rate (periodic rate) is 5%. [Use the two stage binomial method]

Accepted Answer

The answer of Suppose Caroll's stock price is currently $20....

Quiz 21: Valuing Options

A call option on the ABCD stock, with an exercise price of $50, is selling for $5.00 and the stock price is also $50. The call option has a delta of 0.3. If within a short period of time the stock price increases to $52, what would be the change in the price of the call option?

What is the current value of a six-month call option with an exercise price of $12? The Six-month risk-free interest rate (periodic rate) is 5%. [Use the risk-neutral valuation method]

The delta of a put option is always equal to:

Suppose ACC's stock price is currently $25. In the next six months it will either fall to $15 or rise to $40. What is the current value of a six-month call option with an exercise price of $20? The six-month risk-free interest rate is 5% (periodic rate) . [Use the replicating portfolio method]

Suppose ABC's stock price is currently $25. In the next six months it will either fall to $15 or rise to $40. What is the current value of a six-month call option with an exercise price of $20? The six-month risk-free interest rate is 5% (periodic rate) . [Use the risk-neutral valuation method]

Suppose VS's stock price is currently $20. Six-month call option on the stock with an exercise price of $15 has a value of $7.14. Calculate the price of an equivalent put option if the six-month risk-free interest rate is 5% (periodic rate) .

Relative to the underlying stock, a call option always has:

A put option on the ABC stock, with an exercise price of $60, is selling for $4.00 and the stock price is also $60. The put option has a delta of 0.5. If within a short period of time the stock price increases to $61, what would be the change in the price of the put option?

A call option has an exercise price of $100. At the final exercise date, the stock price could be either $50 or $150. Which investment would combine to give the same payoff as the Stock?

Suppose ABCD's stock price is currently $50. In the next six months it will either fall to $40 or rise to $80. What is the current value of a six-month call option with an exercise price of $50? The six-month risk-free interest rate is 2% (periodic rate) .