Interpreting OIS and LIBOR Black-Implied Volatility Quotes
Summary
The document distinguishes volatility quotes by both pricing framework and volatility convention. OIS volatility refers to pricing in a multiple-curve setting, while LIBOR volatility is associated with the older approach in which discounting and forwarding were treated as aligned and basis effects were small. Black volatility means implied volatility recovered using the Black-76 formula; normal volatility refers to inversion under a normal or Bachelier model. Thus, an OIS label does not simply mean replacing one risk-free rate inside an otherwise unchanged Black calculation.
The answer cautions against using OIS volatilities in a traditional LIBOR Market Model without adapting the model to handle multiple curves and basis effects. It notes that market systems can fit and interpolate volatility surfaces in different curve frameworks, and suggests checking consistency by recovering the caplet or swaption prices used as inputs. The discussion is conceptual and does not give a specific instrument quote, calibration procedure, or model implementation.
Key ideas
- OIS and LIBOR volatility quotes reflect different curve and discounting frameworks.
- Black and normal volatility identify different implied-volatility conventions.
- OIS volatility should be matched to a model that represents multiple curves and basis effects.
- Repricing the instruments used to build a volatility surface can help validate the modeling pipeline.
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# What exactly is the OIS Black VOL? # What exactly is the OIS Black VOL? 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 ? ## Answer by experquisite (score 3, accepted) https://quant.stackexchange.com/a/11434 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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