Corn is heavily used in the food industry as livestock feed, starch, corn oil, beverage and industrial alcohol, and fuel ethanol. Given this popularity, you are interested in using the extremely liquid corn forward market to take advantage of possible arbitrage opportunities. Assume that the spot price of 1 bushel of corn (bushel is the unit of how corn is measured in this market) is $150, and that it cost $20 per bushel per 6 months to store the corn. The risk-free rate is 5% per annum with continuous compounding for all maturities.

a- Obtain the forward price of a 13-month forward contract on 1 bushel of corn.

b- Is there any arbitrage opportunity if the market delivery price is $226? Explain why there is or isnt an arbitrage opportunity and the transactions needed to obtain it in case there is.

c- Is there any arbitrage opportunity if the market delivery price is $175? Explain why there is or isnt an arbitrage opportunity and the transactions needed to obtain it in case there is. If the market delivery price is 175, then it is lower than the theoretical fair price. One could think that there is an arbitrage opportunity to take advantage of the low price, however, corn is a consumption asset (implied by the first sentence of the question), therefore owners hold it for its consumption (industrial) value. Owners are not usually willing to sell the assets to buy forwards. This makes the strategy of taking advantage of arbitrage opportunities not feasible.