Natty gas (Natural gas) futures

Suppose it is March 2021 and you are pricing a January 2022 natural gas futures contract that expires in 9 months.

• The current spot price of natural gas is $2.50.
• Suppose that it costs 8% per year to store natural gas.
• The 9-month risk-free rate is 0.30%
• The convenience yield for the January contract is 12%.

a. What is the cost-of-carry for natural gas?

b. What is the no-arbitrage price for the December futures contract?

c. Explain why the convenience yield for the April 2022 natural gas futures contract would be much lower than that of the January 2022 natural gas futures contract? Hint --think seasonality. When is natural gas used the most and why?