Question

What is the price of a European put option on a non- dividend-paying stock when the stock price is $68, the strike price is $70, the risk-free interest rate is 6% per annum, the volatility is 35% per annum, and the time to maturity is six months?

Answer 1

The value of a put option, p of a non dividend paying stock is given by the formula

Where,

S₀ is the current spot rate = 1.50

K is the strike price = 1.45

N(x) is the cumulative normal distribution function

r is the risk free interest rate = 6%

T is the time to maturity = 0.5 years

σ is the volatility = 35%

From the above formulas

d₁ = 0.12783466

d₂ = -0.11965272

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(-0.12783466) = NORMDIST (-0.12783466, 0 , 1, true) = 0.449139912

N(-d₂) = N(0.11965272) = NORMDIST (0.11965272, 0 , 1, true) = 0.5476208716

Implies Value of put option, p = 70*e^-6%*0.5*N(0.11965272) - 68*N(-0.12783466)

= 70*0.9704455335*0.5476208716 - 68*0.449139912

= 37.20053602 - 30.54151401 = $6.65902

Price of put option, p = $6.65902