Question

# Consider an option on a non-dividend-paying stock when the stock price is \$30, the exercise price...

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?

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

d2 =

= 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

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