The Free Boundary SABR: Natural Extension to Negative Rates

In the current low interest rate environment, especially in Japan and Europe where some deposit rates are below zero and many market rates are negative, some firms are finding that their option models do not handle negative rates. Dealing with negative strikes and forwards for short maturity caps and swaptions may require firms to modify their whole implementation of cap and swaption volatility surfaces, so this has become an important issue.
One widely used model, the SABR model, has been extended by practitioners to handle negative rates by adding a deterministic positive shift to a rate and then modeling the shifted rated as a SABR process (“shifted SABR”). While providing realistic probabilities of negative rates, the shifted SABR requires the selection of an arbitrary shift parameter, and it introduces an extra non-calibrated parameter for the SABR model.
So how does one decide what the shift parameter should be? What if rates go lower than the parameter? How will lognormal vols behave near the shift position? Is there a better way to deal with negative rates?

On Thursday, February 26th, 2015 featured speakers Dr. Alexandre Antonov and Dr. Michael Konikov of Numerix discussed how the SABR model can be extended to incorporate a “free boundary” SABR process which more naturally permits negative rates than a shifted SABR process and eliminates the arbitrary lower bound on rates. The free boundary SABR also has the same number of parameters as the classical SABR model, and it includes an efficient and accurate analytical approximation which is crucial for fast calibration.

Dr. Antonov and Dr. Konikov covered:

  • Brief introduction on the SABR model
  • The free boundary SABR as replacement for the shifted SABR
  • Drawbacks of the shifted SABR vs. advantages of the free SABR
  • CEV example (primer for free boundary SABR discussion)
  • Free boundary SABR
  • Exact solution for zero-correlation case (no correlation between a rate and its volatility)
  • Efficient approximation for general correlation case
  • Simulation schemes
  • Practical experiments using European call options
  • Analytical results vs. Monte Carlo simulations

Featured Speakers


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