Question 1

What would have been the cost of a protective put portfolio?

Accepted Answer

The cost of a protective put portfolio is calculated by adding the cost of the underlying asset and the cost of the put option.

Cost of underlying asset = $50
Cost of put option = $1.19 (calculated as $50 x 2.38%)

Total cost = $50 + $1.19 = $51.19

Therefore, the best choice is B.

Question 2

You calculate the Black-Scholes value of a call option as $3.50 for a stock that does not pay dividends but the actual call price is $3.75.The most likely explanation for the discrepancy is that either the option is _________ or the volatility you input into the model is too _________.

Accepted Answer

The actual call price being higher than the Black-Scholes calculated value suggests the option might be overvalued in the market, or the volatility input into the model was too low, leading to an underestimation of the option's value.

Question 3

Suppose you purchase a call and write a put on the same stock with the same exercise price and expiration.If prices are at equilibrium the value of this portfolio is ________.

Accepted Answer

This is a synthetic long stock position, known as a "fiduciary call," which is equivalent to holding the stock and borrowing the present value of the exercise price. The value is S₀ - Xe^-rt.

Question 4

According to the put-call parity theorem,the payoffs associated with ownership of a call option can be replicated by __________________.

Accepted Answer

The answer of According to the put-call parity theorem,the payoffs...

Question 5

You would like to be holding a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
-Suppose the desired put options with X = 50 were traded.What would be the hedge ratio for the option?

Accepted Answer

The hedge ratio (delta) for a protective put is calculated as the change in the option price divided by the change in the stock price. Since the stock can either increase or decrease by 10%, the hedge ratio is -0.5, indicating that for every share of stock, you need half a put option to hedge.

Question 6

Calculate the price of a European call option using the Black Scholes model and the following data.Stock price = $56.80.Exercise price = $55.Time to expiration = 15 days.Risk free rate = 2.5%.Standard deviation = 22%.Dividend yield = 8%.

Accepted Answer

The answer of Calculate the price of a European call...

Question 7

The intrinsic value of an out of the money call option ___________.

Accepted Answer

The intrinsic value of an out-of-the-money call option is zero because the option's strike price is above the current market price of the underlying asset, meaning there is no inherent profit in exercising the option.

Question 8

What combination of variables is likely to lead to the lowest time value?

Accepted Answer

When time to expiration is short, there is less time for the underlying asset to move, and hence less chance for volatility. Low volatility further ensures that the price of the option remains relatively stable, leading to lower time value.

Question 9

Calculate the price of a call option using the Black Scholes model and the following data.Stock price = $47.30.Exercise price = $50.Time to expiration = 85 days.Risk free rate = 3.0%.Standard deviation = 35%.

Accepted Answer

Using the Black Scholes model with the provided data, we get:

d1 = [ln(S/E) + (r + σ^2/2)t] / (σ√t) 
= [ln(47.30/50) + (0.03 + 0.35^2/2)(85/365)] / (0.35√(85/365)) 
= -0.4675

d2 = d1 - σ√t 
= -0.4675 - 0.35√(85/365) 
= -0.8504

N(d1) = 0.3212 
N(d2) = 0.1988

C = SN(d1) - EN(d2) e^(-rt) 
= 47.30×0.3212 - 50×0.1988×e^(-0.03×85/365) 
= $2.22

Therefore, the answer is B, $2.22.

Question 10

You are considering purchasing a put option on a stock with a current price of $33.The exercise price is $35,and the price of the corresponding call option is $2.25.According to the put-call parity theorem,if the risk-free rate of interest is 4%,and there are 90 days until expiration,the value of the put should be ____________.

Accepted Answer

P = C - S0 + Xe−rT or P = 2.25 - 33 + (35)e−(0.04)(90/365) = 3.91

Question 11

The time value of a call option is likely to decline most rapidly ________ days before expiration?

Accepted Answer

The time value of an option declines most rapidly in the last few weeks before expiration, with the sharpest decline occurring in the final 10 days. Therefore, choice A (10 days before expiration) is the best answer.

Question 12

What aspect of the time value of money does the factor of e represent in the Black-Scholes option value formula?

Accepted Answer

The factor of e in the Black-Scholes formula represents continuous compounding, which is a more accurate estimate of the time value of money than annual or daily compounding. Compounding at the expiration time frame is not a relevant factor in the formula.

Question 13

The stock price of Harper Corp.is $33 today.The risk-free rate of return is 6% and Harper Corp.pays no dividends.A put option on Harper Corp.stock with an exercise price of $30 and an expiration date 73 days from now is worth $0.95 today.A call option on Harper Corp.stock with an exercise price of $30 and the same expiration date should be worth __________ today.

Accepted Answer

C = S₀ − Xe−rT + P; C = 33 − (30)e−^(0.06)(0.2)+ 0.95 = 4.308

Question 14

A call option on Juniper Corp.stock with an exercise price of $75 and an expiration date one year from now is worth $3.00 today.A put option on Juniper Corp.stock with an exercise price of $75 and an expiration date one year from now is worth $2.50 today.The risk-free rate of return is 8% and Juniper Corp.pays no dividends.The stock should be worth __________ today.

Accepted Answer

The correct answer is A because the stock price is equal to the exercise price plus the present value of the call option minus the present value of the put option. The present value of the call option is $3.00 / (1 + 0.08)^1 = $2.78. The present value of the put option is $2.50 / (1 + 0.08)^1 = $2.32. Therefore, the stock price is $75 + $2.78 - $2.32 = $69.73.

Question 15

You would like to be holding a protective put position on the stock of Avalon Corporation to lock in a guaranteed minimum value of $50 at year-end. Avalon currently sells for $50. Over the next year, the stock price will increase by 10% or decrease by 10%. The T-bill rate is 5%. Unfortunately, no put options are traded on Avalon Co.
-Suppose the desired put options with X = 50 were traded.How much would it cost to purchase?

Accepted Answer

The cost of the put option can be calculated using the binomial option pricing model. The stock can go up to $55 or down to $45. The risk-neutral probability of the stock going up is (1.05 - 0.9) / (1.1 - 0.9) = 0.75. The expected payoff of the put option is 0.25 * $5 = $1.25. Discounting this at the risk-free rate of 5% gives $1.25 / 1.05 = $1.19.

Question 16

A call option has an exercise price of $30 and a stock price of $34.If the call option is trading for $5.25,what is the intrinsic value of the option?

Accepted Answer

The intrinsic value of a call option is the difference between the stock price and the exercise price. In this case, it is $34 - $30 = $4. The option is trading for $5.25, which includes both the intrinsic value and the time value. Therefore, the intrinsic value of the option is $4, which is given by choice C.

Question 17

The fact that American put values may not equal the price implied by put call parity is attributable to the possibility of what event?

Accepted Answer

American put options can be exercised early, which can affect their value and cause them to deviate from the price implied by put-call parity. The possibility of early exercise causes American put values to be higher than European put values. Changes in dividends and interest rates can also affect option prices, but they do not explain the specific deviation in American put values from put-call parity.

Question 18

A call option has an exercise price of $35 and a stock price of $36.50.If the call option is trading at $2.25,what is the time value embedded in the option?

Accepted Answer

The intrinsic value of the option is the difference between the stock price and the exercise price, which is $1.50 ($36.50 - $35). 
The time value is the difference between the option price and the intrinsic value, which is $0.75 ($2.25 - $1.50). 
Therefore, the answer is B.

Question 19

The stock price of Atlantis Corp.is $43 today.The risk-free rate of return is 10% and Atlantis Corp.pays no dividends.A call option on Atlantis Corp.stock with an exercise price of $40 and an expiration date six months from now is worth $5.00 today.A put option on Atlantis Corp.stock with an exercise price of $40 and an expiration date six months from now should be worth __________ today.

Accepted Answer

The answer of The stock price of Atlantis Corp.is $43...

Question 20

What portfolio position in stock and T-Bills will ensure you a payoff equal to the payoff that would be provided by a protective put with X = $50?

Accepted Answer

In order to replicate the payoff of a protective put with X=$50, we need a portfolio position that will provide us with a minimum payoff of $50 if the stock price falls below $50. One way to achieve this is to have a long position in 0.5 shares of stock and a short position in 0.5 puts with X=$50. The cash generated from the short put can be invested in risk-free T-Bills to earn a return. Calculations show that with the current stock price and risk-free interest rate, $26.19 in T-Bills is sufficient to provide a total payoff of $50 in case the stock price falls below $50. So the correct answer is C.

Quiz 16: Option Valuation