I have a black-Scholes model in excel to calculate Theoretical prices and Greeks. I would like to use this to calculate for american style futures options( Metals, energy and index futures on CME). I was hoping someone with a decent grasp of Option pricing models, could point me in the right direction as to what calculations, or inputs I would need to change to calculate for these? According to my very limited understanding and what I have googled, I need to be following the Black 76 Model and replacing the Spot price (S) with Future price (F)? In this case is the Future price just the Price of the futures contract? Or do I need to make some calculations using this Price to calculate the Future price? Any help with this would be much appreciated
Try this: http://www.cmegroup.com/tools-information/quikstrike.html The basic application is free and there are paid subscriptions from $25/mo to several hundred/mo. CME exchange-traded instruments only. In the basic application you get the model in red. In the paid versions you can choose from: Black76 Generalized Black-Scholes Barone Adesi Whaley '87 (American) Bjerksund Stensland '93 (American) Bjerksund Stensland '02 (American) Normal (Bachelier) Hoadley Trading and Investment Tools is also a good choice, especially if you want to set up your own sheets. Costs about $140 USD. You can find the formulas online, but there are a lot of things in Hoadley beyond the formulas.
I imagine it's overkill to do smth like this for metals and energy futs, since they don't pay divs. So your basic European options calculator should be fine. For the index futs, if you need a general solution, you can probably use one of the American options methods, such as Barone-Adesi & Whaley mentioned above. The best thing you can probably do is buy Espen Haug's reference book on option pricing formulae, as everything is in there.
Brighton, thanks very much. Already had a quick look at this and while the free version would be more than enough, I am aiming for an excel solution as I am looking to automate some position analysis. I am very interested in the Hoadley excel, and that is probably my next option if I can't modify what I have myself.
Martinghoul, thank you! A definite purchase then. In short though, it looks like rather than a small tweak of my black-Scholes excel, I am looking at creating an excel with a different model to calculate these futures options?
MG - For American style futures options on physical commodities, do you have an opinion on the interest rate issue? By that I mean whether plugging in an interest rate is even necessary. Some applications will pre-populate the field with a current rate, increasing it slightly for long dated options, but I've also read (can't source it, but it wasn't a single instance) that the interest rate is unnecessary because it's built into the very structure of a futures market. I realize that for a small trader and at today's interest rates, it doesn't make a lot of difference, but is this a settled matter for larger practitioners? Side note: The more I read and learn, the more I realize that at least in the academic world, what I thought was settled, isn't. In addition to the example above, I recently came across two articles by math professors who did not use LN price changes when calculating the standard deviation of a price series.
Martinghoul, Quick question regarding these models for futures options. They seem to require cost of carry, is there a commonly accepted estimation for these or are these numbers that traders try to get from specific sources and as accurately as possible? Thank you again!
Black-76 d1 = (ln(F / K) + (v ^ 2 / 2) * T) / (v * Sqrt(T)) d2 = d1 - v * Sqrt(T) C = e^(-r * T) * (FND(d1) - KND(d2)) P = e^(-r * T) * (KND(-d2) - FND(-d1))
AFAIK, you do need a rate for the options calcs, regardless of the underlying futures having it "built in" or not (whether they actually do is a rather non-trivial point).
Well, cost of carry is just a single number that represents the total cost (including opportunity cost) that you incur by having a position in something. It depends on what the underlying is, as well as your position and your funding arrangements. You can find a very decent explanation of the concept if you google it. It's gonna be a lot more eloquent than anything I can come up with.