Calibration Methods of Hull-White Model

43 Pages Posted: 29 Nov 2009 Last revised: 31 May 2010

See all articles by Sebastien Gurrieri

Sebastien Gurrieri

affiliation not provided to SSRN

Masaki Nakabayashi

Mizuho Securities Co. Ltd

Tony Wong

affiliation not provided to SSRN

Date Written: November 27, 2009

Abstract

We describe several strategies for the calibration of one factor Hull-White model with constant or time-dependent mean reversion and volatility parameters to the interest rate vanillas.

We propose an efficient approximation formula for the swaption implied volatility which enables us to estimate the mean reversion independently of the volatility.

We give the closed-forms for exact pricing using explicit integrals of the model parameters and propose parametric forms for the mean reversion and volatility. We test their performance in terms of quality of fitting and stability w.r.t. market changes, and show that excellent fits can be obtained without suffering from instabilities. Furthermore, our calibration methods and parameter control techniques allow for an elegant interpretation of market moves, which we illustrate with an in-depth analysis of Lehman crisis in the fall of 2008.

Keywords: Hull-White, calibration, time-dependent, swaption

Suggested Citation

Gurrieri, Sebastien and Nakabayashi, Masaki and Wong, Tony, Calibration Methods of Hull-White Model (November 27, 2009). Available at SSRN: https://ssrn.com/abstract=1514192 or http://dx.doi.org/10.2139/ssrn.1514192

Sebastien Gurrieri (Contact Author)

affiliation not provided to SSRN

Masaki Nakabayashi

Mizuho Securities Co. Ltd ( email )

Tokyo
100-0004
Japan

Tony Wong

affiliation not provided to SSRN

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