Question 1

Consider a one-period binomial model of 12 months.Assume the stock price is $54.00,?σ = 0.25,r = 0.04 and the exercise price of a call option is $55.What is the forecasted price of the stock given an upward movement during the year?

A) $56.16
B) $61.01
C) $65.12
D) $72.16

Accepted Answer

To find the discount rate for a European call option, we need to use the risk-neutral probability, which is given by:
p = (e^(rΔt) - d) / (u - d)
where:
r = risk-free rate = 0.06
Δt = time period = 0.5 years
d = e^(-σ√Δt) = 0.9650
u = e^(σ√Δt) = 1.0350
Plugging in the values, we get:
p = (e^(0.06*0.5) - 0.9650) / (1.0350 - 0.9650) = 0.5395
Using the risk-neutral probability, we can find the expected payoff of the call option at expiration:
E(Payoff) = (Max(0, ST - K)) * p + (Max(0, ST - K)) * (1 - p) / (1 + Y)
where:
ST = stock price at expiration
K = strike price = $45.00
Y = discount rate for the option
Since this is a one-period model, with an up-move of u = 1.0350 and a down-move of d = 0.9650, the possible stock prices at expiration are:
ST(up) = $45.00 * 1.0350 = $46.58
ST(down) = $45.00 * 0.9650 = $43.43
The expected stock price at expiration is:
E(ST) = $45.00 * (1 + 12.0% * 0.5) = $48.60
Using the expected stock price and the up-move and down-move, we can find the expected value of the option at expiration:
E(Payoff) = (Max($0, $46.58 - $45.00)) * 0.5395 + (Max($0, $43.43 - $45.00)) * (1 - 0.5395) / (1 + Y)
E(Payoff) = $1.58 * 0.5395 + $0.00 * (1 - 0.5395) / (1 + Y)
E(Payoff) = $0.8539 / (1 + Y)
Since the option price today is the expected value discounted at the rate Y, we can write:
Option price = E(Payoff) / (1 + Y)
Substituting the values, we get:
$3.77 = $0.8539 / (1 + Y)
Y = $0.8539 / $3.77 - 1 = 0.2264 or 22.64%
Therefore, the answer is B) 39.1% (closest to 22.64% out of the options given).

Question 2

Consider a one-period binomial model of 12 months.Assume the stock price is $54.00,?σ = 0.25,r = 0.04 and the exercise price of a call option is $55.What is the forecasted price of the stock given a downward movement during the year?

A) $43.77
B) $ 45.28
C) $48.98
D) $51.84

Accepted Answer

D

Question 3

Consider a one-period binomial model of 6 months.Assume the stock price is $45.00,?σ = 0.20,r = 0.06 and the stock's expected return is 12.0%.What is the discount rate for a ?$45.00 strike European call option (Y)?

A) 38.2%
B) 39.1%
C) 42.5%
D) 45.6%

Accepted Answer

Using the one-period binomial model, we can calculate the up and down movements of the stock as:

u = e^(σ√(t)) = e^(0.28√(0.5)) ≈ 1.147
d = e^(-σ√(t)) = e^(-0.28√(0.5)) ≈ 0.870

where t= 6 months/12 months = 0.5 years

Next, we can calculate the probabilities of the stock going up and down as:

p = (e^(r×t) - d) / (u - d) = (e^(0.05×0.5) - 0.870) / (1.147 - 0.870) ≈ 0.566

q = 1 - p ≈ 0.434

Therefore, the true probability of the stock going up is 56.6%, which is option A.

Question 4

Under what circumstances should an option be exercised early?

Accepted Answer

The answer of Under what circumstances should an option be...

Question 5

Why is an American call option rarely exercised early,and thus priced similar to European options?&#10;A) Early exercise requires purchasing the stock&#10;B) Most option sellers cannot deliver the stock&#10;C) Option prices usually exceed intrinsic values&#10;D) Short sellers disrupt delivery

Accepted Answer

American call options are rarely exercised early because their price often includes not just the intrinsic value (the difference between the stock price and the strike price), but also time value. Time value represents the potential for further increase in the stock's price. Exercising the option early forfeits this time value, making it financially less advantageous in most cases.

Question 6

What is the relationship between dividends and the forecasted stock price in a binomial model?

Accepted Answer

The answer of What is the relationship between dividends and...

Question 7

Using a binomial pricing model,what is the impact on the price of a call option if the company increases the dividend paid to shareholders? The call option price:&#10;A) Will drop&#10;B) Will increase&#10;C) Will remain constant&#10;D) Impact cannot be determined

Accepted Answer

When the company increases the dividend paid to shareholders, the call option price will drop because the increase in the dividend reduces the value of the underlying stock, which in turn reduces the value of the call option.

Question 8

Ask the class to prove that option pricing is consistent with standard discounted cash flow calculations.Propose that students form groups and develop two binomial trees for the same set of data.One tree should use real probabilities as defined in chapter 11 and the other as defined in chapter 10.

Accepted Answer

The answer of Ask the class to prove that option...

Question 9

A stock price is $85.00.Assume r = 0.07 and there is no dividend.What is the 6-month forward price?&#10;A) $88.03&#10;B) $89.16&#10;C) $90.26&#10;D) $92.33

Accepted Answer

The forward price is calculated using the formula: Forward Price = Spot Price * e^(r*t). Here, Spot Price = $85, r = 0.07, t = 0.5 years. Plugging in the values, Forward Price = 85 * e^(0.07*0.5) = $88.03.

Question 10

When developing a binomial tree model where stocks pay discrete dividends,what problem may occur?

Accepted Answer

The answer of When developing a binomial tree model where...

Question 11

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $46.00,σ = 0.28,r = 0.06 and the dividend yield is 2.0%.What is the maximum approximate strike price where early exercise would occur with an American call option?

A) $29
B) $33
C) $42
D) $46

Accepted Answer

The answer of Consider a two-period binomial model,where each period...

Question 12

In a binomial pricing model,what is the lowest price of an option at any node and why?

Accepted Answer

The answer of In a binomial pricing model,what is the...

Question 13

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $46.00,σ = 0.28,r = 0.06 and the dividend yield is 2.0%.What is the maximum approximate strike price where early exercise would occur with an American call option?

A) $29
B) $33
C) $42
D) $46

Accepted Answer

The answer of Consider a two-period binomial model,where each period...

Question 14

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $46.00,σ = 0.28,r = 0.06 and the dividend yield is 2.0%.What is the maximum approximate strike price where early exercise would occur with an American call option?

A) $29
B) $33
C) $42
D) $46

Accepted Answer

The answer of Consider a two-period binomial model,where each period...

Question 15

Consider a three-period binomial model of 12 months.Assume the stock price is $37.50,?σ = 0.20,r = 0.05 and the exercise price of a call option is $35.What is the forecasted price of the stock at the node after two consecutive upward movements of the stock price?

A) $38.68
B) $42.80
C) $48.84
D) $50.06

Accepted Answer

The answer of Consider a three-period binomial model of 12...

Question 16

What is the primary potential for error when using the Cox-Ross-Rubenstein binomial tree?

Accepted Answer

The answer of What is the primary potential for error...

Question 17

What economic concept is central to proving that risk neutral pricing functions in the establishing of option prices?&#10;A) Consumption possibilities&#10;B) Factor analysis&#10;C) Marginal average cost&#10;D) Declining marginal utility

Accepted Answer

The answer of What economic concept is central to proving...

Question 18

Consider a two-period binomial model,where each period is 6 months.Assume the stock price is $46.00,σ = 0.28,r = 0.06 and the dividend yield is 2.0%.What is the maximum approximate strike price where early exercise would occur with an American call option?

A) $29
B) $33
C) $42
D) $46

Accepted Answer

The answer of Consider a two-period binomial model,where each period...

Question 19

Consider a one-period binomial model of 12 months.Assume the stock price is $54.00,?σ = 0.25,r = 0.04 and the exercise price of a call option is $55.What is the forecasted price of the stock given a downward movement during the year?

A) $43.77
B) $ 45.28
C) $48.98
D) $51.84

Accepted Answer

The answer of Consider a one-period binomial model of 12...

Deck 11: Binomial Option Pricing: Selected Topics