Question

3. 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

Bionomial option pricing model mito r sene 1) The Term Bionomial in the name refer to the two values a Stock can take at the End of the period. 2) This model can be applied whenever we have asset (or) security which can take two values at the end of the period under consideration Herve 1 year Wholding 27. t ad (9-15 Time = Interest ? = rates - option we can find values based 2012: call option. that stuck can take two an on w Increase in price d decrease in price 1 9 - OST = $100 2 Assume market price strike price x cor) Exercise price J price in i year $ 105 y vierno meteot e an @ 20% and increase Decrease solution : cy follows we Su = - = can solve it S (1+u) $100 (1+201) $120 - Increase in I year Sd = (1 d) = $100(1-306) = $70-1) decrease in ferro

we can where we the Stock amount returns adopt Risk assume and in an Neutral that questing asset o valuation approach Invee Investing mo the same i giving 2 tin ut 2015 $120 dites Totoni non cod 220. at $ 100 $70 Let up' be the can stock Probability probability that . take higher value. - Su Cl-p) be the probability that stock can take Lower value. - Sa s tor AS per Risk neutral principle, we match the returing of stock and tigt enterest rate Die we get Colbous as follows xud olor Px 120 + C1-P) 70 = market 2 mprice x interest price s T x time (NOTO) Alternatively we can use CCRY model but for simple understanding I have dore by this way. 120p + 70 - 700 = 100+ 100X2'' x 1 year 50p + 20 = 100 + 2 50p 102-10 rate P = = 32 0.64 - porobability of pris Increate CI-P) = 1-0.64 = 0.36 - probability of decrease

i Call option will have the same probability's as market price in taking upper - and lower values. . Cu = maximum (Su- Exercise price, o) cu = max (120-105,0) cu = 15 a= max (Sa- Exercise price, o) ca = max (70-105,0) ca = o expected value Of - P. Cu + C1-PDEA call option after one year = 0.64 x 15 + 0.36x0 = 9.6 value of call option present value after = one year = 9.6 9.6 TANT 9.6 I + x 9.6 1.02 option 2 = value $9.41176 of Call today