Question

Consider an option on a non-dividend-paying stock when the stock is $ 30, the exercise price is $29. The risk –free rate is 5% per annum, the volatility is 25% per annum, and the time to maturity is four months.

(a) What is the price of the option if it is European call?

(b) What is the price of option if it is an American call?

(c) What is the price of the option if it is a European put?

Answer 1

Solution :

In the question, it is given that S=$30, Strike price = K = 29, Risk-free rate = 5% , Volatility = 25%

The Black-scholes formula and calculation is given in the below excel sheet

.a. The European call price is $2.52

b.The American call price is the same as the European call price. It is $2.52.

c.The European put price is $1.045