Abstract
The discrete-time multifactor Vasiček 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 Vasiček 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 Vasiček models.
Highlights
The tractability of affine models, such as the Vasiček [1] and the Cox–Ingersoll–Ross [2] models, has made them appealing for term structure modeling
Affine term structure models are based on a factor process, which in turn describes the evolution of the spot rate and the bank account processes
Under equivalent martingale measure P∗, the yield curve dynamics (Y (k, ·))k∈N0 obtained by the consistent re-calibration (CRC) algorithm of Section 3.1 has the following Heath–Jarrow–Morton [3] (HJM) representation for m > k + 1: Y (k + 1, m)(m − (k + 1))∆ = Y (k, m)(m − k)∆ − Y (k, k + 1)∆
Summary
The tractability of affine models, such as the Vasiček [1] and the Cox–Ingersoll–Ross [2] models, has made them appealing for term structure modeling. No-arbitrage arguments provide the corresponding zero-coupon bond prices, yield curves and forward rates Prices in these models are calculated under an equivalent martingale measure for known static model parameters. Model parameters typically vary over time as financial market conditions change They may, for instance, be of a regime switching nature and need to be permanently re-calibrated to the actual financial market conditions. This re-calibration is done on a regular basis (as new information becomes available).
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