Question

Consider an option on a non-dividend-paying stock when the stock price is $30, the exercise price is $29, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months. Assume that the stock is due to go ex-dividend in 1.5 months. The expected dividend is 50 cents. Using the Black-Scholes-Merton model, what is the price of the option if it is a European put?

Answer 1

Stock price S₀ = $30

Exercise price K = $29

Interest rate r = .05

= 0.25

T = 4/12

Ex-dividend

The present value of the dividend must be substracted form the stock price

30-0.5e^-0.125*0.05 = 29.5031

d₁ =

=

=0.3068

d_{2 =}

= 0.1625

N(-d₂) = 0.3795,  N(-d₂) =0.4355

We get 0.3795 by using NORMSDIST Function in Excel

=N(-3068) = 0.6205 Same method for N(-d₂)

The Price of option when it is European Put is

29e^-0.05*4/12 * 0.4355 - 29.5031 * .3795 = $1.22