QuoteOriginally posted by: Heshil Hi I am currently trying to price options on eurodollar futures (mid curve options - where the underlying future expires at a later time than the option). I am pricing the option using the modified (call on price = put on yield) black 76 (assuming european). I am having difficulty understanding what volatility to use in the model. Letsigma1 be the vol at time 1 sigma2 be the vol at time 2sigma1-2 be the forward vol from time 1 to time 2Sigma1 and sigma2 are vols where the option expires on the same day as the future.Does anyone know what vol to use for an option that expires at time 1 with an underlying future that expires at time 2?I dont think that its any of the above sincesigma1 ignores vol between 1 to 2simga2 ignores the fact that the option expires earlier (not sure if the t scaling factor in black fixes this)sigma1-2 ignores the vol between 0 and 1thanks for your timeunkpath is right, but I would like to make some distinctions about nomenclature, and set down a conceptual footpath.1) Nomenclature Whereas Rebonato's superb book refers to serial options, Eurodollar Midcurves are not serial options by this definition, and the CME has in fact other products that are called serials. The standard contract cycle in Eurodollars, like a lot of futures markets, is quarterly. So in the front expiration year (i.e. the first four quarterlies), they decided to list some monthly expirations of futures, before and inbetween the first couple of quarterlies. There are options listed on these - they are on serial futures contracts and hence on the floor are referred to as serial options. These options and their underlying futures have abysmal liquidity, and since Eurodollars are probably the most deeply liquid futures on the planet, these things are then doubly damned.The futures are distinguished by a "color code" system of each four quarterlies at a time. The front four are called "white," the next four are called "red," and then "green," and so on. A "Midcurve" option is an option whose underlying is, for instance, June of '09 (red) but the expiration for the option is something like June of '08 (white). A shorthand way of identifying this is to call it "Short June." Similarly, the green-month whose options expire in June '08 is called "Green June." Ambiguity is removed by calling a normal quarterly expiring option against red june futures as "Red June" options. Since green months have no quarterly options, there's no conflict. (Further, the strike is called by its middle two digits. So a 1-Yr midcurve of 9550 puts expiring Jun of '08 is referred to as "Short June 55 Puts," or "Short June Double Puts." Now say that fast while flipping someone off and chewing sunflower seeds, and you are a real floor trader.)2) Structure First of all, Eurodollar futures are not FRAs. Check Hull or anywhere else. There are complications here, so Rebonato's "serial" options are not the same because he is talking about options on forward rates. So how to handle volatility modelling? Realize that our old friend, Black volatility, is an attribute of the underlying. So what's the underlying? Well, for our Short June Double Puts, it's the Red June contract, right? So now what?3) Modeling Knowing the implied volatility of quarterly Red June options, can we simply use the same number for the midcurve? No, because any financial contract - I don't care what it is - has some kind of term structure of volatility to it. So, perhaps we can "time scale" this quarterly number using the formula that you listed. This is fine, and in fact is dicussed in the Collector's excellent books as a way to set bounds on arbitrageability. However lots of folks will tell you that it can be pretty wrong to "scale" volatility like this. (Also I would not call it "forward vol." Most people misuse this term and you don't want to be like most people, do you?) Which brings us to the next point: you need some kind of model that takes this contract, June '09, and somehow tells you what its term structure and skew ought to look like, given the current state of affairs. How you do this is an art form perhaps.Capice?