Questions 1-8should be answered by building a 15-period binomial model whose parameters should be calibrated to a Black-Scholes geometric Brownian motion model with:T=.25years,S0=100,r=2%,=30%and a dividend yield ofc=1%.

Hint

Your binomial model should use a value ofu=1.0395.... (This has been rounded to four decimal places but you should not do any rounding in your spreadsheet calculations.)

(It seems it would be a better choice to usespreadsheet. Thus I would appreciate someone would upload the spreadsheet as well.)

Submission Guidelines

Round all your answers to2 decimal places. So if you compute a price of 12.9876 you should submit an answer of 12.99.

Q1

Compute the price of an American call option with strike K = 110 and maturity T = .25 years.

Q2

Compute the price of an American put option with strike K = 110 and maturity T = .25 years.

Q3

Is it ever optimal to early exercise the put option of Question 2?

Q4

If your answer to Question 3 is "Yes", when is the earliest period at which it mightbe optimal to early exercise? (If your answer to Question 3 is "No", then you shouldsubmit an answer of 15 since exercising after 15 periods is not an early exercise.)

Q5

Do the call and put option prices of Questions 1 and 2 satisfy put-call parity?

Q6

Compute the fair value of an American call option with strike K = 110 and maturityn= 10periods where the option is written on a futures contract that expires after15 periods. The futures contract is on the same underlying security of the previousquestions.

Q7

What is the earliest time period in which you might want to exercise the Americanfutures option of Question 6?

Q8

Compute the fair value of a chooser option which expires after n = 10 periods. Atexpiration the owner of the chooser gets to choose (at no cost) a European call optionor a European put option. The call and put each have strike K = 100 and they mature5 periods later, i.e. atn= 15.