Question

Binomial Model Variables
U	1.15
D	0.90
Index price	PKR720
Strike price	PKR750
Hedge ratio	0.5697
Interest rate	3%

Calculate the price investor paid two years ago for call option with strike price of PKR750 using the binomial valuation method and the data above.

Answer 1

Standard Inputs :

S= Stock price = PKR 720

E = Exercise price = PKR750

U =1.15

D = 0.9

US = 1.15 * 720 = 828

DS = 720*0.9 = 648

U^2S = 1.15*1.15*720 = 952.2

UDS = 1.15*720*0.9 = 745.20

D^2S = 720*0.9*0.9 = 583.2

R = ( 1 + risk free rate ) = 1.03

Risk neutral probability = ( R - D) / ( U -D)

= ( 1.03 - 0.9) / ( 1.15 - 0.9) = P = 0.52

1 - P = 1 - 0.52 = 0.48

payoff from call option = Maxx [ Stock orice - exercise price ,0 ]

payoff in upmove = 952.2 - 750 = 202.20

payoff in down move = 0

Expected payoff = 0.52 * 202.20 + 0.42 *0 = 105.14

Value of call option In year 1 = 105.14 /1.03 = 102.08

expected payoff in year 1 = 102.08 *0.52 + 0.48 * 0 = 53.08

value of calloption 2 years ago = 53.08 /1.03 = 51.54