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Heshil
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Joined: February 22nd, 2008, 4:07 am

Mid curve options

February 28th, 2008, 11:58 am

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 time
Last edited by Heshil on February 27th, 2008, 11:00 pm, edited 1 time in total.
 
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mathmarc
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Joined: March 18th, 2003, 6:50 am

Mid curve options

February 29th, 2008, 3:41 pm

QuoteOriginally posted by: Heshil[BR]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). Maybe you want to use a term structure model to price and manage those options within an IR book. In that case you can have a look atEurodollar Futures and Options: Convexity Adjustment in HJM One-Factor Model.The pricing, including the convexity adjustment, is given in the Gaussian HJM model, which includes as a particular case the extended Vasicek - Hull/White model. Unfortunately you can not calibrate the smile in that model.
 
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PaperCut
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Joined: May 14th, 2004, 6:45 pm

Mid curve options

March 2nd, 2008, 7:10 pm

It looks like the forum reset lost a number of posts since friday - including my reply to this thread. I will reconstruct and re - post soon. Thx
 
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unkpath
Posts: 289
Joined: January 13th, 2004, 8:44 pm

Mid curve options

March 4th, 2008, 2:40 am

hi, exactly it's none of the above. you can look at it this way. the cme introduced these things, sometimes called serial options (as in rebonato) in order to give investors a chance to express views on volatility profile of the underlying. see? before that, there were only full-life options, but it is well known that the volatility of libor is a time-dependent function with certain sylized features. check out burghardt and hoskins' notes for this.later the cme even introduced the so-called weekly options, which allow investors to take even more refined views on the volatility of libor. check out the paper about this on the cme site.the bottom line is that these things are exchange traded, they trade bid-ask fashion. so they represent the market's view of what that volatility profile actually is. there is nothing obvious inherent in the regular options that would allow you to infer the price of the serial option you are interested in, if there were there wouldn't be any point trading those things. if you want to price this option you need a term structure model that you have calibrated with a sensible volatility profile.
 
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PaperCut
Posts: 1616
Joined: May 14th, 2004, 6:45 pm

Mid curve options

March 5th, 2008, 12:38 am

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?
 
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unkpath
Posts: 289
Joined: January 13th, 2004, 8:44 pm

Mid curve options

March 5th, 2008, 2:42 am

1) Midcurve options are serial options according to rebonato's nomenclature. I was never intending to refer to options on serial eurodollar futures. There shouldn't be any confusion though. I apologize for this if there is.But remember eurodollar midcurve options = serial options (in rebonato's sense) on eurodollar futuresnever mind color coding, but you do point out correctly that 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)."2) Eurodollar futures are not FRAs, but settle finally against LIBOR. Eurodollar futures were, as are all futures, introduced by the exchange in order to standardize successfully the corresponding LIBOR contracts which are FRAs. You may read to see in what sense eurodollar futures are related to FRAs/LIBOR.It doesn't matter what rebonato is talking about in terms of underlying. it is understood that the underlying to a eurodollar futures option is a eurodollar and the underlying to an option on a forward is a forward. the point is that what defines the "serial nature" of the optionis that the option expires into an underlying which expires later in time. in this sense mid-curve options are very precisely serial options. futhermore in the US and JP eurodollar options are traded with the premium paid upfront, so doubly damned, these are serial options. in europe on the other hand these options are margined, i.e. they are traded like the underlying and are marked to market. black volatility is irrelevant for any sort of serial option anyway. what matters is that you have a model of the underlying with some assumption for the vol and that you know how to compute the expectation defining your payoff.3) Agreed, you need a term-structure model to be fully consistent. however most houses, I will gamble, will hedge most vanilla productsbased on some extende black-like framework. so in the case of eurodollar options it is not too hard to cook up a shitty theory based on one factor and in the limit repricing the corresponding immediate pay caplet that will be good enough for risk management purposes.
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