Lean hog (LH) futures have been trading in a narrow price range for the past six weeks, and you are convinced that the commodity is going to break far out of that range in the next couple of months. You think its price will go up. The current price of beans is 68.75 cents per pound and the price of a February 2021 call option with an exercise price of $75 cents is 4.5 cents per pound.

(a) If the risk-free interest rate is 2% per year, what must be the price of a February 2021 put option on LH at the same exercise price of $75 cents? Assume 1c/pound/month cold storage costs, and assume full carry (there is plenty of pork meat around).

(b) What would be a simple options-based strategy to exploit your conviction about LH prices future movements? How far would that price have to move (and in which direction) for you to make a profit on your initial investment?

In reality, CME options on livestock are American options. In this question, we assume for simplicity that the option being considered is a European one.