Question

The price of Apple is $197 today. Its annualized volatility in the past year is 20%. Consider a call option expiring in 6 months with strike price K=195. Assume the interest rate is 0.

1. (1) In a one-period binomial tree model, calculate the risk neutral probability q, parameters u

   and d. Recall that u = e?√? and d = e−?√?, where ? is the annualized volatility and T is

   period in years.

2. (2) Calculate the price of the call option in this one-period model

3. (3) Calculate the price of the call option in a two-period model (note that in this case, T is 3

   months instead of 6 months, so you have to re-calculate q, u and d)

4. (4) Extra credit: using computer programs or by hand, compute the option price under a 5-

   period binomial tree model (5pts, and the total score on this problem set cannot exceed 100)

Answer 1

										Price at expiry	Pay off	Probability
										270.272712	75.2727123	0.02661316
								253.708493
						238.159445				238.159445	43.1594455	0.14175346
				223.563354				223.563354
		209.861813				209.861813				209.861813	14.8618132	0.15100832
197				197				197
		184.926449				184.926449				184.926449	0	0.16086741
				173.592851				173.592851
						162.953856				162.953856	0	0.17137018
								152.966894
										143.592003	0	0.03651173
										Value of call at expiry=		10.3655032
										Value of call today=		10.3655032