Question

1. Assume the Black-Scholes framework. The 1-year futures price for stock LMN is $270. The volatility is 30%, and the interest rate is 4%. What is the price of a 280-strike call option price on the LMN futures contract, expiring 9 months from today?

Answer 1

We use Black-Scholes Model to calculate the price of the call option.

The price of a call option is:

C = (S₀ * N(d₁)) - (Ke^-rt * N(d₂))

where :

S₀ = current spot price

K = strike price

N(x) is the cumulative normal distribution function

r = risk-free interest rate. This is 4%, or 0.04.

t is the time to expiry in years. This is (9/12), or 0.75.

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

d₂ = d₁ - σ√T

σ = standard deviation of underlying stock returns

First, we calculate d₁ and d₂ as below :

• ln(S₀ / K) = ln(270 / 280). We input the same formula into Excel, i.e. =LN(270 / 280)
• (r + σ²/2)*T = (0.04 + (0.30²/2)*0.75
• σ√T = 0.30 * √0.75

d₁ = 0.1054

d₂ = -0.1544

N(d₁) and N(d₂) are calculated in Excel using the NORMSDIST function and inputting the value of d₁ and d₂ into the function.

N(d₁) = 0.5420

N(d₂) = 0.4386

Now, we calculate the price of the call option as below:

C = (S₀ * N(d₁))   - (Ke^-rt * N(d₂)), which is (270 * 0.5420) - (280 * e^{(-0.04 * 0.75)})*(0.4386)    ==> $27.1416

Price of call option is $27.1416