A 1-year European call option on a stock with a continuous dividend rate of 2%

~ "u" = upmove factor = Stock price in upmove/Current stock price = 60/50 = 1.20

~ "d" = downmove factor = Stock price in downmove/Current stock price = 40/50 = 0.80

~ "P" = probability of upmove:

= (e^(r-div)t - d) / (u - d)

where,

e = 2.7183

r = risk free rate

div = dividend yield

t = time to maturity

= (2.7183^{(0.05-0.02)x1} - 0.80) / (1.20 - 0.80)

= 0.23045 / 0.40

P = 0.576

~ (1 - P) = Probability of downmove:

= 1 - 0.576

(1-P) = 0.424

~ "fu" = payoff on upmove = pay off if stock price is 60 = Stock price-Exercise price = 60-55 = 5

~ "fd" = payoff on downmove = pay off if stock price is 40 = Not exercised = Payoff is zero.

~ Option premium:

= [ P x fu + (1-P) x fd ] x e^-(r-div)t

= [0.576x5 + 0.424x0] x 2.7183^{-(0.05-0.02)x1}

= [2.88 + 0] x 0.970445

= 2.7949

= 2.79

Answer: Option premium = 2.79