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While poking around in Bloomberg I stumbled upon the following data set: EUR SWPT BVOL OIS for various maturities.

Obviously OIS must suggest OIS-discounting but how is it related to the Black-Implied-Volatility ? Does one simply use the OIS-rate instead of the LIBOR rate as the risk-free reference rate when inverting Black's Formula ?

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Have you tried <HELP> ? I know it sounds stupid but it is often very effective. –  lmorin May 22 at 14:46
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I agree that this is volatility implied by using OIS as a r.f. rate. Since the crises, there is a push to replace LIBOR with OIS as the "true" risk free rate, so this is probably one of the results. –  DatamineR May 22 at 21:00
    
Agree with DatamineR, please see my answer to another question: quant.stackexchange.com/questions/11400/… –  Matt Wolf May 23 at 6:31
    
okey - could perhaps someone convert his/her comment into a genuine answer (perhaps with a reference to some OIS related papers) :D –  Probilitator May 23 at 9:24
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And to answer your first question, some people still quote LIBOR vols, but most caps and swaptions seem to be quoted on an OIS dual-curve-stripped basis. On Bloomberg, they probably tick out both OIS and LIBOR flavors of vols for all the main swaption points, so you shouldn't have a problem as long as you use the compatible vol for your model. A good test would be to see how well your LMM recovers the caplet/swaption prices that go into your terminal vol cube, if there's a disconnect between LIBOR vs OIS or Black vs Normal, your prices should be way off. –  experquisite May 25 at 8:23

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up vote 2 down vote accepted

Reformatting for an answer:

  • OIS (vols) - vols backed out of/for pricing in the presence of multiple curves
  • LIBOR (vols) - vols backed out of/for pricing in the 'old' way where discount=forward and basis is negligible
  • Black (vols) - Black-76 inverted volatilities
  • Normal (vols) - Normal/Bachelier (?) inverted volatilities

FINCAD primer on the 'new curves math': http://papers.ssrn.com/sol3/papers.cfm?abstract_id=2311745

One would not want to drop an OIS vol into an old LIBOR Market Model, but Fabio Mercurio and others have extended LMM to encompass multiple curves with deterministic or stochastic basis functions. http://papers.ssrn.com/sol3/papers.cfm?abstract_id=1621547

Various parties quote vols both coming from a LIBOR- or an OIS- space, the Bloomberg function VCUB fits a volatility surface and interpolates and ticks out vols in both OIS- and LIBOR- spaces. Hovering over the various grid points on the various pages of VCUB should be a good place to start for pulling in vols into your own LMM model. A good test of whether you are using the right vols in the right places (and of everything else in your pipeline) is to try and recover the prices/premia of caplets/swaptions that you initially fed into VCUB. And as others have mentioned, being persistent on <HELP> can quickly get you in touch with some very knowledgeable people.

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I also found the Mercurio paper you mentioned: papers.ssrn.com/sol3/papers.cfm?abstract_id=1621547 –  Probilitator May 25 at 8:43
    
perhaps you could add to your answer :) –  Probilitator May 25 at 8:44
    
Do you knoe whether there is a way to convert an OIS vol the standard LIBOR-one ? –  Probilitator Jun 3 at 9:12
    
Yes, there is a way, but I am not aware of a easy way - the only way I am aware of is to price all the swaptions with the OIS vol to get their premium, then restrip them back to LIBOR vols. EDIT: that said, I don't know why you would need to, BBG has all the Libor vols too. EUSV011 Curncy vs EUVE11 Curncy for instance (LIBOR vs OIS) –  experquisite Jun 3 at 19:20

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