I've just started working for a company with a decent commodity exposure. They manage this by as they call it dynamically hedging it. Basically when they start the hedging they identify a market price and a budget price x% above the market. This budget price is the maximum they are willing to pay on average for the commodity. To achieve this they hedge a percentage of the portfolio and increase this if prices go up and decrease this when prices go down. I'm pretty convinced by this strategy they replicate buying an option at the strike of the budget price but I'm struggling to mathematically prove this. Any help?