# How do you calculate price of non-existant call option on commodity future

I've been stumped on this for awhile now.

I'm trying to determine the price of a call option on a commodity futures contract that expires in the future. My issue is that while the future's contracts are traded 3 years into the future, the options are only actively traded 6 months into the future. I'd like to determine the price of a call option on a future that expires 1 year from now.

I've tried using multiple approaches in R from lognormal curves to exponential and nothing quite cuts it.

Is this possible? How do traders determine the price of an option with no volume?

Any tips, hints, or anything that can lead me into the right direction would be appreciated.

• Hi Curt and Curt, welcome to Quant.SE! Please refer to this help page to get your accounts merged. That will allow you to edit your question from your new account. Commented Sep 22, 2015 at 21:40

The real world scenario you are describing as far as I understand it is a trader writing an OTC call option. His price has to reflect the current and expected future price/movement/volatility of the underlying, namely the commodity future.

Lets first assume that the likely buyer of that option is interested in a a) ATM/ITM option or at least not too OTM, otherwise the premium will be likely too low for the writer to even bother going ahead with the transaction, and b) in an expiry on or near enough an underlying future's maturity (that should not be a problem as most commodities future markets offer maturities for days/weeks or at least monthly ones if they are traded 3 years into the future).

Since there is no daily implied volatility published by a body like an exchange (e.g. LME, SGX, CBOE, etc) one could use as a substitute the historical (aka realised) volatility plus a (il)liquidity reserve. There are several ways to calculate historical volatility using the underlying future prices (Close on Close, OHLC, look up Parkinson, Garman-Klass, volatility cones, etc).

Finally, addressing b) above again: what if the option's maturity can't 'fit' against any liquid traded future (i.e. you dont have an exact/near enough underlying price or time to maturity) ? Not a scenario I have read about or experienced but my guess would be that the underlying future price would be interpolated linearly from known points of the forward curve. Not sure if we are talking contango/backwardation (or even if we are talking perishable or storable commodities here...) but I guess the curve shape (spot out to 3 years) should allow linear interpolation somehow.

Please note that I am also assuming from the question that we are talking 'vanilla' call option, therefore any 'standard' BS or Black76 or similar pricing method could apply assuming you have the necessary inputs described above.

You need to value your option by using any of the known methods. And then add a spread that will value the risk and the unknown volume. This also take us to the point that it will be traded over the counter. That means that will be a bilateral agreement with the two counterparties.

What I will do is value it with a similar process to valuing a swaption, divide the valuing of the option in two parts:

• First, the value of the option after the trading period.

• Discount the value of the first step, and then calculate the value of it.(I would use montecarlo for this two steps)

As a summary, I would value it with the same method as a swaption, changing the value of the swap for the value of your option.