Question

Shares in ABC plc are currently trading at $5 per share. The share has volatility of 22% per annum and the risk-free rate of interest is 1.5% per annum. According to the Black-Scholes-Merton (1973) approach, what is the delta of an at-the-money, 3-month European put option written on one ABC share. (DETAILED WORKINGS PLEASE)

a. -0.5355

b. -0.464505

c. 0.535495

d. 0.508341

e. -0.49166

Answer 1

Given for ABC shares,

current price S0 = $5

Volatility sd = 22%

risk free rate = 1.5%

for at-the money 3 month option,

strike price K = spot price = $5

T = 0.25

So, using Black-Scholes-Merton model, d1 = (ln(S0/X) + (r + (1/2)*(sd^2))*T)/(sd*(T^(1/2)))

=> d1 = (ln(5/5) + (0.015 + (1/2)*(0.22^2))*0.25)/(0.22*0.25^0.5) = 0.089090909

So, Delta of a call option = N(d1) = N(0.089090909) = 0.535495

So, delta of a put option = N(d1) - 1 = 0.535495-1 = -0.464505

Option b is correct

N(d1) is calculated on excel using function =Normsdist(0.089090909)