## Option Pricing - Multi Period Binomial Model

manan.shah77
Posts: 2
Joined: Mon Nov 09, 2015 7:49 am

### Option Pricing - Multi Period Binomial Model

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

u = 1.0395

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=110 and maturity T=.25 years.
3. Is it ever optimal to early exercise the put option of Question 2?
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?
6. Compute the fair value of an American call option with strike K=110 and maturity n=10 periods where 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.
7. What is the earliest time period in which you might want to exercise the American futures option of Question 6?
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.

manan.shah77
Posts: 2
Joined: Mon Nov 09, 2015 7:49 am

### Re: Option Pricing - Multi Period Binomial Model

Okay, so I have worked my way towards building the lattice and got answers to all but two (#6 and #8) questions -

1. American Call = \$2.60
2. American Put = \$12.37
3. Yes, it is optimal to exercise (dividend is present at c=1%)
4. Exercise at period number 5.
5. No, the Put-Call parity hasn't been satisfied.
6. ------------------
7. Found by trial and error - period number 7 (although I would like to seek an explanation)
8. ------------------