Question

For a European 3-month call option, you are given:

(1) The price of the underlying stock is 50.

(2) The strike price is 48.

(3) The stock pays no dividends.

(4) σ=0.25σ=0.25.

(5) r=0.06r=0.06.

Calculate the elasticity of the call option.

Answer 1

Elasticity of a call option is the delta of the call option.

Delta = N(d₁)

d₁ = (ln(S₀ / K) + (r + σ²/2)*T) / σ√T

where :

S₀ = current spot price

K = strike price

r = risk-free interest rate

T is the time to expiry in years

σ = standard deviation of underlying stock returns

N(x) is the cumulative normal distribution function

First, we calculate d₁ as below :

• ln(S₀ / K) = ln(50 / 48). We input the same formula into Excel, i.e. =LN(50/48)
• (r + σ²/2)*T = (0.06 + (0.25²/2)*0.25
• σ√T = 0.25 * √0.25

d₁ = 0.5091

N(d₁) is calculated in Excel using the NORMSDIST function and inputting the value of d₁ into the function.

N(d₁) = 0.6947

Elasticity of the call option is 0.6947