The variance-minimizing hedge with put options

Certain commodity producers face uncertain output and price, but can trade financial derivatives on price. I consider how best to use a put option on price. I introduce the variance surface, which is a data visualization technique that shows the level of variance across a grid of values for the two choice variables, quantity of options and strike price. The variance-minimizing hedge has strike deep in the money and optimal quantity close to expected output, but the variance surface shows there are near-best choices that are less expensive.