Question 1

In a one-period binomial model with S_u = 49.5, S_d = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth? A) 2.17 B) 0.50 C) 9.50 D) 5.00 E) none of the above

Accepted Answer

The answer of In a one-period binomial model with S_u...

Question 2

In a recombining binomial model with n periods, the number of outcomes is n + 1.

Accepted Answer

In a recombining binomial model with n periods, the number of outcomes is equal to the number of ways that k successes can occur in n trials, which is (n choose k) + 1. Since k ranges from 0 to n, there are n+1 possible outcomes.

Question 3

Determine the value of d for a four period binomial model when the option's life is one-fourth of a year and the volatility is 0.64. Use the model for u and d that does not require the risk-free rate.
A) 0.85
B) 1.17
C) 2.56
D) 0.90
E) none of the above

Accepted Answer

Using the formula, 
d = e^(-σ√(t/n)) 
where σ is the volatility, t is the time period (in years), and n is the number of periods per year. 
Substituting the given values, we get: 
d = e^(-0.64√(0.25/4)) 
d = 0.85 (rounded to two decimal places) 
Therefore, the answer is A) 0.85.

Question 4

All of the following are variables used to determine a call option's price except
A) the risk-free rate
B) the probability of stock price movement
C) the exercise price
D) the possible future stock prices at expiration
E) none of the above

Accepted Answer

Although the probability of stock price movement can influence an investor's decision to purchase a call option, it is not a variable used to determine the option's price. Instead, the primary variables used to price call options are the risk-free rate, exercise price, and possible future stock prices at expiration.

Question 5

The binomial probabilities are probabilities if investors were risk neutral.

Accepted Answer

The binomial probabilities are calculated under the assumption that investors are risk-neutral, meaning they are indifferent towards risk and only care about expected return.

Question 6

When the hedge ratio is adjusted in the binomial model, the transactions must be done in the option.

Accepted Answer

In the binomial model, adjusting the hedge ratio typically involves transactions in the underlying asset, not necessarily in the option itself. The hedge ratio determines the proportion of the underlying asset to be bought or sold to hedge the option position.

Question 7

Pricing a put with the binomial model is the same procedure as pricing with a call, except that the
A) underlying stock must not pay dividends
B) binomial model cannot account for expiration payoffs
C) value of the underlying must be discounted back to the current time period
D) expiration payoffs reflect the fact that the option is the right to sell the underlying stock
E) none of the above

Accepted Answer

Pricing a put option with the binomial model involves calculating the expected payoffs at expiration, which reflect the fact that the option is the right to sell the underlying stock at a predetermined price. Therefore, the correct answer is D. Choice A is incorrect because the binomial model can handle dividends, as long as the dividend payments are known and incorporated into the calculation. Choice B is incorrect because the binomial model is designed specifically to account for expiration payoffs. Choice C is incorrect because the value of the underlying must be discounted back to the current time period for both call and put options in the binomial model. Choice E is incorrect because there is a correct answer.

Question 8

The hedge ratio is the number of shares per call in a risk-free portfolio.

Accepted Answer

The answer of The hedge ratio is the number of...

Question 9

The binomial model assumes that investors are risk neutral.

Accepted Answer

The binomial model does not assume that investors are risk neutral. It allows for the incorporation of risk preferences through the use of a risk-adjusted discount rate.

Question 10

If there is one period remaining and no possibility of the option expiring in-the-money, the hedge ratio will be zero.

Accepted Answer

If there is no possibility of the option expiring in-the-money, there is no need for hedging and therefore the hedging ratio will be zero.

Question 11

The binomial option pricing model will converge to what value as the number of periods increases?
A) a random value
B) the Black-Scholes-Merton value of the option
C) the intrinsic volatility of the option
D) the true value of the underlying
E) none of the above

Accepted Answer

The binomial option pricing model is a discrete-time model that assumes that the price of the underlying asset can move up or down in each period. As the number of periods increases, the model will converge to the continuous-time Black-Scholes-Merton model, which is the industry-standard for pricing options. Therefore, the value calculated by the binomial model will converge to the Black-Scholes-Merton value of the option.

Question 12

The up and down factors in the binomial model are analogous to the volatility.

Accepted Answer

The up and down factors in the binomial model represent changes in the stock price, much like how volatility represents changes in the stock price in the Black-Scholes model. So, the statement is true.

Question 13

Which of the following statements about the binomial model is incorrect?
A) it converges to the Black-Scholes-Merton model
B) it can accommodate early exercise
C) it allows only two stock prices at expiration
D) it can be extended to a large number of time periods
E) none of the above

Accepted Answer

The binomial model allows for any number of stock prices at expiration, not just two.

Question 14

Determine the value of u for a three period binomial problem when the option's life is one-half a year and the volatility is 0.48. Use the model for u that does not require the risk-free rate.
A) 1.22
B) 1.48
C) 1.40
D) 1.32
E) none of the above

Accepted Answer

The answer of Determine the value of u for a...

Question 15

A riskless hedge involving stock and puts requires a long position in stock and a short position in puts.

Accepted Answer

A riskless hedge involving stock and puts typically requires a long position in stock and a long position in puts, not a short position in puts. This strategy is known as a protective put, where the put option provides downside protection.

Question 16

In the binomial model, if a call is overpriced, investors should sell it and buy stock.

Accepted Answer

If a call is overpriced, it means that the option's price is higher than what is justified by the underlying stock's price and the strike price. In this case, investors should sell the overpriced call option and buy the underlying stock. This is because selling the call option generates a premium, which can offset some of the costs of buying the stock, while buying the stock allows investors to profit from a potential increase in the stock's price.

Question 17

All of the following are practical applications of the binomial model except
A) choices regarding real options
B) options regarding executive incentive plans
C) models in which the stock price can go up, down, or remain constant in the next period
D) embedded options within debt securities
E) none of the above

Accepted Answer

The binomial model is used for options pricing and assumes that the price of the underlying asset can only move to two possible values over any short time period (up or down), not remain constant.

Question 18

Which of the following statements about the binomial option pricing model is not always true?
A) it can capture the effect of early exercise
B) it can accommodate a large number of possible stock prices at expiration
C) it reflects the effects of the stock price, exercise price, risk-free rate, volatility and time to expiration
D) it gives the price at which the option will trade in the market.
E) none of the above

Accepted Answer

The binomial option pricing model gives a theoretical price for the option based on the inputs, but it does not necessarily give the price at which the option will trade in the market. The market price may be higher or lower depending on supply and demand, as well as other factors such as liquidity and transaction costs.

Question 19

One way to model an option with dividends in the binomial framework is for the stock price minus the present value of the dividends to grow by the up and down factors.

Accepted Answer

This is the correct way to model an option with dividends in the binomial framework, as the dividends reduce the stock price and must be accounted for in the option valuation.

Question 20

A stock priced at 50 can go up or down by 10 percent over two periods. The risk-free rate is 4 percent. Which of the following is the correct price of an American put with an exercise price of 55?
A) 7.88
B) 3.38
C) 4.00
D) 5.00
E) 1.65

Accepted Answer

The answer of A stock priced at 50 can go...

Quiz 4: Option Pricing Models: The Binomial Model

In a one-period binomial model with Su = 49.5, Sd = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?

In a recombining binomial model with n periods, the number of outcomes is n + 1.

Determine the value of d for a four period binomial model when the option's life is one-fourth of a year and the volatility is 0.64. Use the model for u and d that does not require the risk-free rate.

All of the following are variables used to determine a call option's price except

The binomial probabilities are probabilities if investors were risk neutral.

When the hedge ratio is adjusted in the binomial model, the transactions must be done in the option.

Pricing a put with the binomial model is the same procedure as pricing with a call, except that the

The hedge ratio is the number of shares per call in a risk-free portfolio.

The binomial model assumes that investors are risk neutral.

If there is one period remaining and no possibility of the option expiring in-the-money, the hedge ratio will be zero.

The binomial option pricing model will converge to what value as the number of periods increases?

The up and down factors in the binomial model are analogous to the volatility.

Which of the following statements about the binomial model is incorrect?

Determine the value of u for a three period binomial problem when the option's life is one-half a year and the volatility is 0.48. Use the model for u that does not require the risk-free rate.

A riskless hedge involving stock and puts requires a long position in stock and a short position in puts.

In the binomial model, if a call is overpriced, investors should sell it and buy stock.

All of the following are practical applications of the binomial model except

Which of the following statements about the binomial option pricing model is not always true?

One way to model an option with dividends in the binomial framework is for the stock price minus the present value of the dividends to grow by the up and down factors.

A stock priced at 50 can go up or down by 10 percent over two periods. The risk-free rate is 4 percent. Which of the following is the correct price of an American put with an exercise price of 55?

In a one-period binomial model with S_u = 49.5, S_d = 40.5, p = 0.8, r = 0.06, S = 45 and X = 50, what is a European put worth?