Problem B3 The Black Scholes Merton Model 18 marks Consider an option on a non dividend paying stock when the stock price is $29, the exercise price is $30, the risk free interest rate is 5 per annum, the volatility is 25 per annum, and time to maturity is five months Notes Keep four decimal points for and Use the Table for with interpolation in calculating and What is the price of the option if it is a European call 4 marks What is the price of the option if it is an American call 2 marks What is the price of the option if it is a European put 4 marks If it is an American put, can you use the Black Scholes Merton Model to calculate the price If not, briefly discuss some other approach to value this option 2 marks If this is a European call and there is a dividend of $1 50 expected in two months, what is the price of the option 4 marks If this is a European call and there is a dividend of $1 50 expected in six months, what is the price of the option 2 marks

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Question: Problem B3: The Black-Scholes-Merton Model [18 marks] Consider an option on a non-dividend-paying stock when the stock price is $29, the exercise price is $30,

Problem B3: The Black-Scholes-Merton Model [18 marks]

Consider an option on a non-dividend-paying stock when the stock price is $29, the exercise price is $30, the risk-free interest rate is 5% per annum, the volatility is 25% per annum, and time to maturity is five months. Notes: Keep four decimal points for and . Use the Table for with interpolation in calculating and .

What is the price of the option if it is a European call? [4 marks]
What is the price of the option if it is an American call? [2 marks]
What is the price of the option if it is a European put?[4 marks]
If it is an American put, can you use the Black-Scholes-Merton Model to calculate the price? If not, briefly discuss some other approach to value this option. [2 marks]
If this is a European call and there is a dividend of $1.50 expected in two months, what is the price of the option?[4 marks]
If this is a European call and there is a dividend of $1.50 expected in six months, what is the price of the option? [2 marks]

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