1.

a) What is the payoff of a European put option if the strike price is 50 and the value of the underlying asset at the expiry date is 30? b) What is the payoff of a European call option if the strike price is 70 and the value of the underlying asset at the expiry date is 45?

c)Suppose that in the fixed interest rate model the interest rate compounded yearly has the continuous distribution RUniform(1.2%,2.7%). What us the probability that 100 accumulates to less than 105 after three years? State your answer as a decimal to three significant figures

2.

Suppose that a broker quotes the price of unit zero-coupon bonds, with maturity times of (0.5,1.0,1.5,2.0) years, to be respectively (0.93,0.90,0.84,0.82).

Calculate the no-arbitrage price of a 2-year bond with face-value 750,000, semi-annual coupons at rate 2% per annum, and redeemable below par at exactly half its face value. State your answer to the nearest pound. Do not enter the pound sign.