Question

Use a one step binomial option pricing model to value a 1 year at the money call option on AT&T. Assume interest rates are 2%. How does your value compare with the market price?

Answer 1

The volatility calculated from last 5 year stock prices of AT&T using logarithmic method is 0.1467 and the rate is assumed to be 2%. The stock price as of 29^th November,2019 is 37.56

The up price in the model is

=S0 * e^(Volatility*Sqrt(t))

=37.56 * e^0.1467

=43.50

The down price in the model is

=S0 * e^(-Volatility*Sqrt(t))

=37.56 * e^-0.1467

=32.43

Probability of price going up is:

P=(e^rt – d)/(u-d)

Calculating the same:

P=0.53

The following table shows the Call option price for 1 year at various strike prices:

Option Up are the returns in case of price going up, similarly option down is the return from the option in case of the price going down.

Strike Price	Option up	Option Down	P * Option Up	(1-P) * Option Down	Total	Option Price= Total * E^-r
43	0.50	0.00	0.23	0.00	0.23	0.23
42	1.50	0.00	0.70	0.00	0.70	0.69
41	2.50	0.00	1.17	0.00	1.17	1.15
40	3.50	0.00	1.64	0.00	1.64	1.60
39	4.50	0.00	2.10	0.00	2.10	2.06
38	5.50	0.00	2.57	0.00	2.57	2.52
37	6.50	0.00	3.04	0.00	3.04	2.98
36	7.50	0.00	3.51	0.00	3.51	3.44
35	8.50	0.00	3.98	0.00	3.98	3.90
34	9.50	0.00	4.44	0.00	4.44	4.36
33	10.50	0.00	4.91	0.00	4.91	4.82
32	11.50	0.43	5.38	0.23	5.61	5.50

The actual Call Option prices are 4.1 for strike price of 35 as compared to 3.9 in our calculation and the same for 37 is 2.9 as compared to 2.98 in our calculation and at strike price of 40 it is 1.75 as compared to 1.6 in our calculations.