Calibration Methods of Hull-White Model

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. ∗email: [email protected] §email: [email protected] ¶email: [email protected]