Question

a company's stock is currently trading at $20.  The stock has an expected return of 5% and a standard deviation of 20%. Assume the risk-free rate is 2%. For the 6-month call option with a strike price of $20, what is the option elasticity?

Answer 1

Option's elasticity is the change in a price of an option given a 1% change in the price of the stock

The option Greek 'Omega' measures the option's elasticity.

Omega = Delta * Price of the stock/ Price of the option

First, we calculate the price of the call option using Black-Scholes model

The strike price K=$20

S(0) = $20

r = 0.02

t = 0.5

d1 = (ln(20/20) + (0.02+ (0.2*0.2/2))*0.5)/(0.2*(0.5^0.5))

d1 =0.1414

d2 = 0.1414- (0.2*(0.5^0.5) = -0.0000213

Delta N(d1) = 0.55623

N(d2) = 0.5

c = 20*0.55623 - 0.5*20*e^(-0.02*0.5)

c = 1.224

Omega = Delta * Price of the stock/ Price of the option

Omega = 0.55623*20/1.224= 9.089

Omega = Option's elasticity = 9.089%