solve

1. It's August, a bond with semiannual coupons and matures in one year is selling for $80, the next coupon of $2 is due in October. The risk-free interest rate is 2% p.a. continuously compounded for all maturities. The 5-month forward contract on this bond with physical delivery is selling for $76.5. Are there arbitfage opportunities to be exploited? If so, lay out the opportunity in full with detailed explanations and exact cash flows at each step. ( 9 marks) II. It's August, wheat is currently trading at $380 /tonne. Wilson Farms expects to harvest wheat in January 2023 and decides to take positions in ASX Jan '23 Eastern wheat futures to hedge against price volatility. The futures is trading at $387/ tonne. In October, the futures price has increased to $390 /tonne while the spot price is $385/ tonne. In January 2023 , the contract trades at $400/ tonne just before the last trading day on contract. (a) Describe the type of hedge used and the position entered in August. ( 2 marks) (b) Calculate the basis in August and then in October. (2 marks) (c) Assume the market is free of arbitrage in January 2023, the farm closes its futures positions and cash settles just before the last trading day while it simultaneously trades on the spot market. Assume the underlying is a perfect match for the farm, explain the steps of how the hedge is closed, show cash flows at each step, and calculate the net effective price for the farm. (5 marks) (d) Suppose the farm instead used forward contracts that required physical delivery and each contract is on 100 metric tonnes. Based on past observations, the farm expects 1000 metric tonnes of wheat might be harvested. Should the farm hedge with 10 contracts? Why or why not