Question

A stock has an asset price of $50. Bobby and Christine both believe the stock will go up 20% one year or it will go down 20% one year from now ($40 or $60) <-- I am assuming either one of those is the answer. Bobby believes the probability of the stock going up to $60 one year from now is only 70%, while Christine believes the probability that it will go up to $60 in a year which is only 30%. If the risk free rate of return is 3.5%, what is the value of the call option one year from now?

Answer 1

Strike Price : $ 50

R(Rate factor) = (1+r) = 1.035

d (Downfactor) = 120/100 = 1.20 (100 is considered as stock price just to calculate these factors)

u (Upfactor) = 80/100 = 0.80

Pu (Payoff from call option if stock goes up = $ 10)

Pd (Payoff from call option if stock goes down = 0)

Probability that stock will go up (P) = (R - d)/ (u - d)

= (1.035 - 0.80)/(1.20 - 0.80)

= 0.235/0.40

= 58.75 %

Value of Call option = { Pu*(p) + Pd*(1-P) } / (1 + r)

= (10*(0.5875) + 0)/1.035

= $ 5.68