Posted: June 30th, 2022

Evaluate Sensitivities of Bermudan Adaptions

Evaluate Sensitivities of Bermudan Adaptions

The Hull White interest rate model is one of the classical interest rate models in finance. It was proposed in [HW90] as an extension of the Vasicek model. The model yields analytical formulas for bonds and European bond options. With time inhomogeneous model parameters it can be fitted to an observed term structure of interest rates and a term structure of volatilities. The resulting calibrated model can then be used to price more exotic interest rate derivatives. Particular financial derivatives priced by the Hull White model are Bermudan bond options and Bermudan swaptions.

The evaluation of sensitivities in the Hull White model with respect to changes in the yield curve (i.e. Deltas and Gammas) are discussed, e.g. in [Hen04]. Risk sensitivities of Bermudan swaptions (also with a focus on changes in the yield curve) are elaborated in.

Key risk factors for Bermudan swaptions are market observed Black’76 volatilities of European swaptions. Hence the sensitivity of the price with respect to changes in the volatility is of particular interest. A market standard method for sensitivity evaluation is bumping the input risk factors, re-evaluate the derivative price and compute a finite difference approximation of the sensitivity. This approach may not work appropriately for Bermudan swaption since the pricing involves an iterative calibration procedure and a numerical solution on a PDE grid (or a tree) which both introduce numerical errors.

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