Question

What are the deltas of a call option and a put option with the following characteristics? (A negative answer should be indicated by a minus sign. Do not round intermediate calculations and round your answers to 4 decimal places, e.g., 32.1616.)

Stock price = $40

Exercise price = $35

Risk-free rate = 4.9% per year, compounded continuously

Maturity = 9 months

Standard deviation = 60% per year

Call option delta= ?

Put option delta= ?

Answer 1

Delta of call option = 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 maturity in years

N(x) is the cumulative normal distribution function

We calculate d₁ as below :

• ln(S₀ / K) = ln(40 / 35). We input the same formula into Excel, i.e. =LN (40 / 35)
• (r + σ²/2)*T = (0.049 + (0.60²/2)*0.75
• σ√T = 0.60 * √0.75

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

N(d₁) = 0.7216.

Delta of call option = 0.7216

Delta of put option = N(d₁) - 1

Delta of put option = 0.7216 - 1

Delta of put option = -0.2784