Task

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

I

Task

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

Instructions

Use your textbook to answer the following questions from Chapter 12:

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.

(c) What is the early-exercise premium?

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?