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 use spreadsheet. Thus I would appreciate someone would upload the spreadsheet as well.)

Submission Guidelines

Round all your answers to 2 decimal places. So if you compute a price of 12.9876 you should submit an answer of 12.99.

Q1

Option Pricing in the Multi-Period Binomial Model | Coursera

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

Q2

Option Pricing in the Multi-Period Binomial Model | Coursera

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

Q3

Option Pricing in the Multi-Period Binomial Model | Coursera

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

Q4

Option Pricing in the Multi-Period Binomial Model | Coursera

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

Option Pricing in the Multi-Period Binomial Model | Coursera

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

Q6

Option Pricing in the Multi-Period Binomial Model | Coursera

Compute the fair value of an American call option with strike K = 110 and maturityn = 10 periods 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

Option Pricing in the Multi-Period Binomial Model | Coursera

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

Option Pricing in the Multi-Period Binomial Model | Coursera

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. at n = 15.