(a) It is 1 January 2021. The 90 day bank bill yield to maturity is a 2.625% p.a. simple interest rate. The 180 day bank bill yield to maturity is a 2.670% p.a. simple interest rate. The futures exchange quote for a 90 day bank bill futures contract maturing in 90 days time is Q=97.41

Using this information, compute

(i) the yield to maturity (expressed as an annual simple rate of interest) implied by the futures quote of 97.41, and the equivalent continuously compounded annual rate of interest

(ii) the delivery price of a 90 day bank bill futures contract with a face value of $1m and a term of 90 days based on that yield

(iii) the price of a 90 day bank bill with a face value of $1m as at 1 january

(iv) the price of a 180 day bank bill with a face value of $1m as at 1 january

(v) the forward interest rate on a 90 day loan, taken out in 90 days time on 1 april 2021 and maturing on 30 june 2020, expressed as a continuously compounded rate.W 3 What combination of 90 day and 180 day ZCBs is equivalent to a forward contract maturing in 90 days to sell a 90 day ZCB?

(vi) the price of a 90 day bank bill with a face value of $1m implied by this forward interest rate

(vii) is there an arbitrage opportunity implied by this information?

(viii) If so how could we exploit it? (assume a futures contract on a bill is equivalent to a forward contract on a bill for the purpose of answering this part of the question.

(ix)Suppose you are short the bank bill futures contract described above on 1/1/2021 and that this futures contract matures on 1/4/2021 and the bank bill you would obtain by exercising the futures contract matures on 30/6/2021. Over the next two days the bank bill futures quote (for a bill futures maturing on 1/4/2021) changes to 97.20 on 2/1/2021 and then to 97.10 on 3/1/2021.

Compute the change in the delivery price of the bill futures resulting from these changes to the futures quotes.

Compute the variation margin you as the holder of the bill futures contract would have to pay to the exchange clearing house as a result.

(x) On 3/1/2021 you decide to close out your short bank bill futures contract. What does this involve? What type of futures position do you have to take in order to close out the long futures? What futures

contract trade do you need to do?