Question

The current data of Eastern Baltican Steel (EBS )are as follows: Current share price: 54 €, Strike price: 56 €, Volatility: 45%, Maturity of the option: 2 years, short rate: 3%.
Could you please calculate for your mother the fair call option-price
(i) using a binomial tree (time step 1 year)
(ii) using the Black-Scholes Formula.

Answer 1

(i) Binomial tree

u = e^(0.45*(1^0.5)) ; = 1.57

d = 1/u ; = 0.64

= (e^(0.03*1) - 0.64)/(1.57-0.64) ; = 0.42

therefore the prediction of the Spot at time of maturity:

St = $84.78 (54*1.57) or $34.56 (54*0.64)

Payoff in the both the scenario = if(St-K>0,St-K,0); then, Payoff = ( $28.78 , 0 ) = (fu,fd)

therefore the present value of future payoff as the portfolio is considered as the delta neutral= ƒ = [ pƒu + (1 – p)ƒd ]e–rT

= (e^(-0.03*1))*(0.42*28.78 + 0.52*0)

= $11.73

(ii)

d1 = (ln(54/56) + (0.03 + 0.2025/2)*1)/(0.45*(1^0.5)) ; = 0.2108

d2 = 0.2108 - 0.45*(1^0.5) ; = -0.2391

N(d1)	0.5835
N(d2)	0.4055
N(-d1)	0.4165
N(-d2)	0.5945

above figurea re botained from the excel function = NORMSDIST()

Thus substituting the above values to the equation mentioned in the first figure of the this section.

we get,

c= $9.4732