Journal of Computational Finance

Risk.net

Bermudan swaption model risk analysis: a local volatility approach

Juliusz Jabłecki

  • This paper is a step-by-step guide for assessing model-based mis-pricing in Bermudan swaptions.
  • It provides an (almost) model-free estimate of the price of a Bermudan swaption with 2 exercise dates based on a calibrated non-parametric interest rate local volatility surface.
  • It offers a static replication of the deferral premium in 2-exercise Bermudan swaptions

Prices of callable interest rate derivatives, such as Bermudan swaptions, can be strongly affected by our choice of interest rate model as well as its parameterization and calibration strategy. This paper develops a simple way to handle the inherent model uncertainty. The approach is based on analyzing the exercise deferral premium of Bermudan swaptions with exactly two exercise dates in a “minimal” nonparametric local volatility interest rate model. It is shown that the value of the right to defer exercise once, at a future call date, depends on the inputs obtained from a calibrated nonparametric local volatility model and can, moreover, be decomposed into a portfolio of standard European swaptions. Such a “fair” price can then be compared with one obtained using a calibrated Bermudan Monte Carlo pricer, yielding a practical way of handling the model risk involved in the chosen Bermudan pricer. Numerical examples from the US dollar swaption market are provided.

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