3. Derivatives Contracts (12 marks)

Q3 1) Bitcoin (BTC) is currently quoted at USD $40000 per unit. The riskless interest rate is 1.5% p.a. annually compounded. BTC can be purchased/sold in fractions (i.e. you can purchase 0.1 BTC in the spot market).

a) Sarah bought 0.5 BTC 5 years ago and has held on to the investment since. She knows she will need to convert her investment to cash a year from now as she would like to use that money for a home down payment. However, she is afraid the current plummeting in BTC price might affect her investment. Which position (long or short) should she take in the futures market to hedge the price risk of BTC? (1 mark)

b) Micro Bitcoin futures traded on the CME have a contract size of 0.1 BTC. What should be the arbitrage-free futures price for the delivery of 0.1 BTC in a years time given the going price for 1BTC and the risk free rate? (1 mark)

c) If Sarah observes a 1-year futures price of Micro Bitcoin futures $4,092.00, explain how she can set up an arbitrage strategy to make a riskless profit (provide details including all the cash flows now and 1 year from now). (4 marks)

Q3 2) Current share price of ABDC Corp is $53. Given his forecasts of the future share value, Stephen wrote two call options on ABDC at a strike price of $50 and bought two call options one with strike price of $45, the other $55. Information on the options can be found in the table below:

Option Type	Exercise Price	Premium
Call	45	$7.29
Call	50	$4.46
Call	55	$2.50

All options are European options and have ABDC Corp as underlying; all options have identical maturities.

In the table below, tabulate the profits of Stephens investment strategy (S_T stands for the share price of ABDC at option maturity; the payoff and profit can be a function of S_T).

a) What is the maximum profit? What about maximum loss? (5 marks)

	ST < 45	45 < ST < 50	50 < ST < 55	ST > 55
payoff
profit

b) What is Stephens expectation of the share price of ABDC Corp, given his investment strategy? (maximum 2 sentences) (1 mark)