The current spot price of grain is $347.75. Assume that the standard deviation of monthly changes in the spot price of grain is 1.1. The standard deviation of monthly changes in grain futures price for the closest contract is 1.6. The correlation between the futures price changes and the spot price changes is 0.8. It is now October 12. Company A is committed to purchasing 300 metric tons of grain a month from now. The firm wants to hedge its risk using the December 2022 wheat futures contracts. Each contract is for the delivery of 50 metric tons of grain.

1. Calculate grain's one-month and one-year Futures prices, assuming the risk-free rate is 4%.
2. What strategy should Company A management follow given its commitment described above? Show all calculations involving the strategy.
3. Should Company A have any concerns if they use the forwards market instead to hedge their risk?

Company A management is considering using some idle cash to purchase options. They approached a trader and obtained the following information about a call and a put.

• Both options have a strike price of $40
• Both options have a maturity date of 6-months
• The cost (premium) of the call is $2, and the put is $1.5
• The current price of the underlying share is $42.
• The volatility is 20%
• The risk-free rate is 10%

4. Calculate the break-even and maximum profit of long positions in the call and put and identify when these strategies (long call; long put) are convenient.

5. If Company A expects an increase in the underlying asset's price, should it invest in a call or a put? What price should be paid for the option based on the Black-Scholes model? Show calculation steps.