Question

Use the Black-Scholes model to find the price for a call option with the following inputs: (1) current stock price is $30, (2) strike price is $36, (3) time to expiration is 6 months, (4) annualized risk-free rate is 7%, and (5) variance of stock return is 0.16. Do not round intermediate calculations. Round your answer to the nearest cent.

Answer 1

Current stock price, S₀ = spot price = $30

Strike Price, K = $36

Time to expiration = 6 months = 0.5 years

risk free rate = 7%

Variance of stock return = 0.16

standard deviation of stock return, σ = Square root of variance = 0.4

The value of a call option, c is given by the formula

Where,

S₀ is the current spot price = $30

K is the strike price = $36

N(x) is the cumulative normal distribution function

r is the risk free interest rate = 7%

T is the time to maturity = 0.5 years

σ is the volatility = 0.4

From the above formulas

d₁ = -0.379439

d₂ = -0.662282

cumulative normal distribution function, N(x) is calculated using NORMDIST function in spreadsheet

NORMDIST (x, mean , standard deviation, cumulative)

Where

x = input to the normal distribution function

mean = mean of normal distribution function = 0

standard deviation = standard deviation of normal distribution function = 1

cumulative = whether to use normal cumulative distribution function rather than distribution function = true

N(d₁) = N(-0.379439) = NORMDIST (-0.379439, 0 , 1, true) = 0.352181

N(d₂) = N(-0.662282) = NORMDIST (-0.662282, 0 , 1, true) = 0.253895

Implies Value of call option,

c = 1.739570

Price of call option, c = $1.74