QUESTION 2 (40 MARKS)

(a) Use the Black-Scholes-Merton model to calculate the prices of European call on an asset priced at $68.50. The exercise price is $65, the continuously compounded risk-free rate is 4%, the options expire in 110 days, and the volatility is 0.38. There are no cash flows on the underlying. [5 Marks]

(b) For a two-period binomial model, you are given the following information:

Each period is one year.

The current price for a non-dividend-paying stock is $35.

. u = 1.2840, where u is one plus the rate of capital gain on the stock per period if the stock price goes up.

d = 0.8607, where d is one plus the rate of capital loss on the stock per period if the stock price goes down.

The continuously compounded risk-free interest rate is 6%.

Calculate the price of an American call option on the stock with a strike price of $38. [15 Marks]

(c) A loan of 584,000 is repayable by equal quarterly payments for 3 years. The effective rate of interest is 7% pa.

REQUIRED (i) Find the equal quarterly payment amount. [3 Marks]

(ii) Draw the amortization schedule for the loan repayment. [10 Marks]

(iii) What is the interest portion paid on the 5th payment? [1 Mark]

(iv) What is the total interest paid after the 7th payment? [2 Marks]

(v) What is the outstanding capital amount after the 10th payment? [2 Marks]

(vi) What is the total amount of capital already repaid before the 8th payment? [2 Mark)