On April 1st, the 6-month forward price for a Treasury Bill (to be paid on October 1st) that pays 1$ of face value on January 1st (the year after) is 0.99. On April 1st, the spot price for bills of the same face value and maturing on October 1st and January 1st is 0.98 and 0.975, respectively. a. Calculate the arbitrage-free treasury-bill forward price (the market price of this forward is 0.99, as mentioned above). In your calculation, highlight what is the arbitrage-free forward interest rate from October 1 to January 1. b. Is there an arbitrage opportunity at these prices? If so, describe two arbitrage strategies that either give you an arbitrage profit on April 1st or on October 1st. How are the arbitrage profits on these two dates related? c. You have given out a floating-rate loan of 1 million $ maturing on January 1st. The interest rate for the final three months to be received on January 1st is set on October 1st. Describe how the interest rate risk of this position can be hedged assuming that the Treasury Bill forward is correctly priced (i.e., use the no-arbitrage price calculated in a.). Show in a table that from the point of view of January 1st the hedge works well for a range of interest rates that can be realized on October 1st.

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