Would you help me solve the question?

Quiz instruction :

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 rounding in your spreadsheet calculations.)

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.

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

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

3.Is it ever optimal to early exercise the put option of Question 2? YES or NO.

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

5. Do the call and put option prices of Questions 1 and 2 satisfy put-call parity? YES or NO.

6.Compute the fair value of an American call option with strike k=100 and maturity periods n=10where the option is written on a futures contract that expires after 15 periods. The futures contract is on the same underlying security of the previous questions.

8.Compute the fair value of a chooser option which expires after n=10 periods. At expiration the owner of the chooser gets to choose (at no cost) a European call option or a European put option. The call and put each have strike k=100 and they mature 5 periods later, i.e. at n=15.

I am really confuse about the question, as no videos online shows how to solve Black-Scholes problem by example. It is a really difficult question for me, please show me very step particularly.

Thanks