Chapter 12 | Accounting homework help

Essay Help

Task

In this assignment, you will solve problems on Binomial Option Pricing.

Instructions

Use your textbook to answer the following questions from Chapter 12:
1. Exercise 16, 17, 18, 19.
Please, upload xls, xlsx file.
Please, use the full computing power of Excel.

16. When there are no dividends, the early exercise of an American put depends on a tradeoff

between insurance value (which comes from volatility) and time value (a function

of interest rates). Thus, for example, for a given level of volatility, early exercise of the

put becomes more likely if interest rates are higher. This question provides a numerical

illustration

Consider a two-period binomial model with u = 1.10 and d = 0.90. Suppose the initial

stock price is 100, and we are looking to price a two-period American put option with

a strike of K = 95.

(a) First, consider a “low” interest rate of R = 1.02. Show that early exercise of the

American put is never optimal in this case.

(b) Nowconsider a “high” interest rate of R = 1.05. Showthat it nowbecomes optimal

to exercise the put early in some circumstances. What is the early exercise premium

in this case?

17. Consider a two-period example with S = 100, u = 1.10, d = 0.90, R = 1.02,

and a dividend of $5 after one period. Is early exercise of a call optimal given these

parameters?

18. We repeat the previous question with higher volatility and interest rates and with lower

dividends. Consider a two-period binomial tree with the following parameters: S = 100,

u = 1.20, d = 0.80, and R = 1.10. Suppose also that a dividend of $2 is expected

after one period.

(a) Compute the risk-neutral probability in this world.

(b) Find the tree of prices of an American call option with a strike of 100 expiring in

two periods.

19. The payment of a dividend on the underlying stock increases the value of a put option

since it “lowers” the stock price distribution at maturity. This question provides a

numerical illustration.

Let a two-period binomial tree be given with the following parameters: S = 100,

u = 1.10, d = 0.90, and R = 1.05. Consider a two-period American put option with

a strike of 90. Note that this put is quite deep out-of-the-money at inception.

(a) What is the value of the American put given these parameters?

(b) Now suppose a dividend of $4 is paid at the end of the first period. What is the new

price of the put?

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July 1, 2023

13.3 Efficiency, Price, and Value

1) The maximum price a consumer is willing to pay for an extra unit of a good or service when total utility is maximized is known as

A) demand.

B) marginal benefit.

C) quantity demanded.

D) total utility.

E) marginal utility.

2) Jen consumes 5 CDs and 2 tacos. She receives 500 units of utility from her 5th CD and 200 units of utility from her 2nd taco. The price of a CD is $10, the price of a taco is $4, and she is spending her entire budget. Which of the following is true regarding Jen's choices?

A) Jen is consuming on her demand curve for tacos.

B) Jen is maximizing utility.

C) Jen is consuming on her demand curve for CDs.

D) Only answers A and B are correct

E) Answers A, B, and C are correct.

3) The fact that diamonds have a much higher price than water

A) violates the rules of utility maximization because water is necessary for life.

B) does not violate the rules of utility maximization because globally, fresh water is actually very rare.

C) does not violate the rules of utility maximization because water's marginal utility is low.

D) violates the rules of utility maximization because diamonds are not necessities.

E) violates the rules of utility maximization because the consumer actually consumes a large amount of water.

4) Which of the following is the best statement of the paradox of value?

A) Why does the amount people are willing to pay for a good vary with the amount consumed?

B) Why do some goods like water, which is necessary for life, have a low price while other goods like diamonds have a high price?

C) What is the logical relationship between value and price?

D) Why is efficiency so valuable for a society?

E) None of the above states the paradox of value.

5) To resolve the paradox of value, you must

A) compare price elasticities of demand across goods.

B) distinguish between marginal and total utility.

C) sacrifice efficiency.

D) minimize consumer surplus.

E) distinguish between marginal utility and price.

6) The solution to the paradox of value is found by looking at which of the following?

A) total usefulness of different goods

B) the difference between marginal utility and total utility

C) relative prices and total utility

D) the difference between marginal utility and price

E) None of the above helps solve the paradox of value.

7) One reason why the price of diamonds is so high is because the

A) marginal utility of diamonds is zero.

B) marginal utility of diamonds is high.

C) marginal utility of diamonds is low.

D) total utility of diamonds is low.

E) total utility of diamonds is high.

8) Why does the paradox of value between diamonds and water arise?

A) because water has a low price and a low total utility, while diamonds have a high price and a high total utility

B) because water has a low price and a low marginal utility, while diamonds have a high price and a high marginal utility

C) because necessities like water are higher priced than luxuries like diamonds

D) because diamonds have a higher value to people even though water is essential to life

E) because water has a low price and a low total utility, while diamonds have a high price but also a low total utility

9) Related to the paradox of value, which of the following statements is correct?

A) The marginal utility of water is enormous but the total utility is small.

B) We consume so much water so its marginal utility is enormous.

C) The marginal utility of water is small but the total utility is enormous.

D) The consumer surplus from water is small.

E) The total utility of water is equal to the marginal utility of water.

10) The paradox of value with respect to water and diamonds can be explained using consumer surplus because

A) water is cheap but provides a large consumer surplus, while diamonds are expensive with a small consumer surplus.

B) diamonds are in large supply relative to their demand, while water is scarce in supply relative to its demand.

C) water is cheap but provides a small consumer surplus, while diamonds are expensive but provide a large consumer surplus.

D) the total consumer surplus from diamonds is greater than the total consumer surplus from water.

E) None of the above answers is correct.