LIBOR based interest rates are derived from the prices (supply / demand) of swaptions, caps and floors.

These prices are generally quoted in yield vols. Their prices are given by the Black formula.

The Black formula assumes the same yield vol. for all ATM and OTM strikes. However, this is a faulty assumption.

What is the process in determining the OTM and ATM volatility skew for a LIBOR market model?

  • $\begingroup$ Where do you get that the prices are quoted in yield vols? I don't trade rate markets (Commods for me) but everything is generally quoted in price terms - if you give a "vol price" it has to make assumptions to get to the vol - what if your assumptions are different? I would be surprised if the market was quoted in vol terms - can you check? $\endgroup$ – will Apr 18 '19 at 21:12
  • $\begingroup$ @will is correct. Those are quoted in price terms. The participants translate the prices into normalized basis point vols. Black lognormal vols are not generally used. $\endgroup$ – dm63 Apr 19 '19 at 13:34
  • $\begingroup$ @will I recently read this: "Swaption and cap prices are often quoted in yield volatility. Consider a 5×10 swaption struck at-the-money at 5% quoted with a yield volatility of 20%. This volatility implies that a one-standard-deviation move over one year of the five-year forward ten-year swap rate would be 5% × 0.2 = 1%. The pricing of these swaptions is then given by the celebrated Black formula." $\endgroup$ – VVKK77 Apr 23 '19 at 14:19
  • $\begingroup$ @will I also read this as a justification: "The market volatility of interest rates is directly correlated to the value of caps and swaptions. The more volatile the market expects interest rates to be, the more valuable these securities are. To avoid constant repricing during the trading day as rates move up or down, the prices of these securities are often quoted as yield volatilities, which are more stable." $\endgroup$ – VVKK77 Apr 23 '19 at 14:54

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