Hedging the gas price - the cost of insurance

I was wondering lately what it would cost to hedge my fuel costs by buying options on oil futures. Chrysler offered something similar with its $2.99 per gallon deal a few weeks ago - I already estimated that cost in a previous post. So I set out this afternoon and did some research, i.e. collecting data from the Energy Information Administration, doing some (dull) regressions, and analyzing option prices. The result is a neat little table (see below) that contains rough estimates for the insurance costs depending on maturity (of the underlying future) and level of protection above which the "insurance" kicks in.

The insurance itself works as follows: You buy call options on oil futures (see below) and when the gas price rises above our protection level the value of the options we bought will have increased and will offset the additional fuel cost (by selling them). Note, that I do not consider transaction costs here which might be significant (especially if you only sell a small volume). Neither, did I consider discounting of the future contracts or convenience yield effects as their impact here is limited although they are important for longer maturities in general.

So how do we come up with some reasonable numbers for costs? The idea is pretty straightforward:

a) Relate gas prices to oil prices: Since a barrel of oil contains 42 gallons the relation should be straightforward from the theoretical point of view. Doing a regression, depending on the grade and the region in the US we obtain that approximately

gas-price-per-gallon (y) = 1.45 + 0.024 oil-price (x)

I actually adjusted the coefficients a bit to reflect the fact that "1/42 * price-per-barrel" is a lower bound for the price of a gallon.

b) Assume that an option is $1 in-the-money. According to the above formula the gas price p.g. increased by $0.024. Therefore we need 0.024 options to offset that increase by selling off the option.

Combining that with latest quotes for call options on oil futures we can calculate:

1) The expected gas price given the underlying oil price. That is the information in the top rows and is the strike price for the option and our protection level.

2) We can calculate the hedging cost for a gallon depending on the maturity of the underlying future contract. Implicitly that determines the expiration of the option as well as it usually expires a few weeks earlier.

The two tables below contain the absolute and the relative (to the protection level) hedging costs.



For example insuring with a protection level of $4.66 a gallon would cost us $0.22 or 4.62% extra (per gallon) if we want this protection for buying fuel until 08/2009. If we want to buy protection for a later point in time, say until 02/2009 we would pay $0.42 or 9.05% premium.

In order to use this strategy more efficiently for hedging exposure we could buy a mix of options to reflect the fact that if we want to fill up the car next week we do not need options with expiration in 05/2009 which are almost twice as expensive as the ones that expire in 08/2009 as we pay a higher time value.

Or we could just drive less... ;-)