Effective Duration with Recalibrated Interest Rate Models

Summary

The document describes a finite-difference approach to effective duration for an interest rate instrument with optionality. The practitioner prices the instrument using a model calibrated to a discount curve and at-the-money swaption volatilities, shifts the curve up and down while keeping the volatility quotes fixed, recalibrates after each shift, and estimates duration from the price difference divided by the original price and twice the curve bump.

Its focus is a reliability problem: an optimizer initialized at the original model parameters may converge to a different parameter set after a curve bump, even when the new fit appears close. Such parameter variation can contaminate the sensitivity estimate. The document reports no proposed validation procedure or empirical results; it mentions a paper that perturbs original parameters instead of recalibrating, but gives no details. The discussion therefore identifies a calibration stability concern rather than resolving it.

Key ideas

• Effective duration can be estimated from prices under up and down discount curve bumps.
• The described workflow recalibrates the rate model after each bump while holding swaption volatility quotes constant.
• Optimizer starting values do not guarantee that recalibrated parameters remain comparable to the original fit.
• Parameter changes can make the resulting duration or other sensitivities unreliable.
• A cited alternative perturbs original model parameters rather than recalibrating, but the document does not explain its method.

Tags

# Effective duration and recalibration


# Effective duration and recalibration












I am calculating the effective duration of an interest rate instrument with optionality. I do the following

- calibrate an interest rate model to market data: discount curve and ATM swaption vols

- use the calibrated model to price the instrument (P)

- bump the discount curve up by dr

- recalibrate the interest rate model (with new curve but unchanged ATM swaption vols)

- price the instrument again (P+)

- repeat with bump down to get P-

- estimate effective duration as (P+ - P-)/(2P dr)

Potential problem: when I recalibrate I use an optimization procedure with initial point set to the parameters from Step 1 and hope that the recalibrated model parameters are close to these. This is what seems to happen but there is no real guarantee that this will happen and even if the recalibrated parameters appear to be close to the originals, they may be sufficiently different to give unreliable values for the effective duration.

How do people try to ensure that the recalibrated parameters are reliable for calculating the effective duration (or any sensitivity, for that matter)?

The only reference that I've found on the topic is a paper by Joshi and Kwon where they develop a method to perturb the original parameters instead of recalibrating:

Joshi_Kwon_parameter_perturbation

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.