Question

What is the price of a European put on a non-dividend-paying stock when the stock price is $79, the strike price is $77, the continuously compounded risk-free interest rate is 6% per annum, the volatility is 25% per annum, and the time to expiration is eight months?

Answer 1

Answer:

The price of an European Put Option = $4.03

Explanation:

Hi, you have to use a formula for the evaluation of an European put option on an underlying, which does not pay dividends. This equation follows the Black & Scholes-Merton model.

This is the model for a put option

$p(s,t)=-SN(-d1)+Ke^{-rt}N(-d2)$

N(-d1) is the cumulative normal distribution function, calculated as follows.

$d1 =\frac{Ln(S/K)+(r+\frac{sigma^{2}}{2})t  }{sigma\sqrt{t} }$

for N(-d2) yoou have to make the following calculation

$d2=d1-sigma\sqrt{t}$

where:

K = Opcion strike price

N = Standard normal cumulative distribution function

r = Risk Free interest rate

σ = Volatility of the underlying

S = Price of the underlying

t = Time to option´s expiry

Here are the result of all the above calculations

S= $79.00    

K= $77.00    

r = 6% annual  

sigma =25% annnual  

t = 0.67  years (That is 8/12 to turn months into years )

d1 = 0.42  

d2 = 0.22  

N(-d1) = 0.335913098

N(-d2) = 0.41312295

e^(-rt) = 0.960789439

 

p(s,t)= - 79(0.3359...) + 77(0.9607...)(0.413122...) = $4.03

Notice the excel spreadsheet attached.

best of luck .