Consistent Re-Calibration of the Discrete-Time Multifactor Vasi\v{c}ek Model

TL;DR

This paper introduces a consistent re-calibration method for the discrete-time multifactor Vasicek model, enabling it to adapt to changing market conditions while maintaining no-arbitrage properties, demonstrated through Swiss interest rate fitting.

Contribution

It develops a CRC approach for the multifactor Vasicek model, allowing for time-dependent parameters while preserving tractability and no-arbitrage conditions.

Findings

Successfully fits Swiss interest rates with CRC Vasicek models.

Maintains no-arbitrage property in re-calibrated models.

Provides a practical framework for dynamic interest rate modeling.

Abstract

The discrete-time multifactor Vasi\v{c}ek model is a tractable Gaussian spot rate model. Typically, two- or three-factor versions allow one to capture the dependence structure between yields with different times to maturity in an appropriate way. In practice, re-calibration of the model to the prevailing market conditions leads to model parameters that change over time. Therefore, the model parameters should be understood as being time-dependent or even stochastic. Following the consistent re-calibration (CRC) approach, we construct models as concatenations of yield curve increments of Hull-White extended multifactor Vasi\v{c}ek models with different parameters. The CRC approach provides attractive tractable models that preserve the no-arbitrage premise. As a numerical example, we fit Swiss interest rates using CRC multifactor Vasi\v{c}ek models.