Question

What is the price of a European call option on a non-dividend-paying stock when the stock price is $60, the strike price is $60, the risk-free interest rate is 10% per annual, the volatility is 20% per annual, and the time to maturity is 1 year. Round d1 and d2 to two decimal points.

Show all work. Do not use an online option price calculator.

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

T is the time to expiry in years

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(60 / 60). We input the same formula into Excel, i.e. =LN(60 / 60)
• (r + σ²/2)*T = (0.10 + (0.20²/2)*1
• σ√T = 0.20 * √1

d₁ = 0.60

d₂ = 0.40

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) = 0.7257

N(d₂) = 0.6554

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

C = (S₀ * N(d₁))   - (Ke^-rT * N(d₂)), which is (60 * 0.7257) - (60 * e^{(-0.10 * 1)})*(0.6554)    ==> $7.96

Price of call option is $7.96