Question

Consider a call option written on a non-dividend-paying stock when the current stock price is $35, the exercise price is $30, the risk-free interest rate is 5% per annum, the volatility is 35% per annum, and the time to maturity is 4 months.

a) What is the price of a European call option written on the stock?

b) What is the price of an American call option written on the stock?

c) Assume that the stock will pay a dividend in 2 months. The expected dividend is 60 cents. What is the price of a European call option written on the dividend-paying stock?

Please show all your steps to the solution.

Answer 1

PART-A

Considering 2 Period Binomial Tree

4-Month Euro Call option

The price of the option is $6.429

The Formula used are:

PART-B

4-Month American Call option

The price of the option is $5.868

The Formula used are:

PART-C

4-Month Euro Call option with dividend

The price of the option is $6.267

The Formula used are:

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