On the Generation of Negative Yields Under the Vasicek One-Factor Model

Abstract

The generation of yield curves is performed in many contexts, e.g. for the valuation capital requirement (under banking and insurance regulation frameworks ) as well as the pricing of the financial contracts. The famous Vasicek one-factor model can be applied for such a purpose. It plays the role of a benchmark, mainly due to its tractability, but it always generates negative yields for the zero-coupon bond which are economically unacceptable.In this paper, we analyse to what extend this model can be used to interest rates term structures at a future time horizon, given this inconsistency resulting from negative interest rates. Both theoretical analyses and empirical observations are performed here to shed light the reader about the difficulties underlying any Gaussian Affine Term Structure Model. No close look to these difficulties is really available in the literature to the best of our knowledge, despite the importance of such extended models in the generation of interest rate scenarios.