Arbitrage-free models bond yields

An arbitrage-free model of the term structure on the other hand can be made to fit precisely with the current, observed term structure, so that observed bond yields are in fact equal to the bond yields calculated by the model. So, an arbitrage-free model is intended to be consistent with the currently observed... 

In this chapter, we have considered both equilibrium and arbitrage-free interest-rate models. These are one-factor Gaussian models of the term structure of interest rates. We saw that in order to specify a term structure model, the respective authors described the dynamics of the price process, and that this was then used to price a zero-coupon bond. The short-rate that is modelled is assumed to be a risk-free interest rate, and once this is modelled, we can derive the forward rate and the yield of a zero-coupon bond, as well as its price. So, it is possible to model the entire forward rate curve as a function of the current short-rate only, in the Vasicek and Cox-Ingersoll-Ross models, among others. Both the Vasicek and Merton models assume constant parameters, and because of equal probabilities of forward rates and the assumption of a normal distribution, they can, xmder certain conditions relating to the level of the standard deviation, produce negative forward rates. 

The Vasicek model was the first term-structure model described in the academic literature, in Vasicek (1977). It is a yield-based, one-factor equilibrium model that assumes the short-rate process follows a normal distribution and incorporates mean reversion. The model is popular with many practitioners as well as academics because it is analytically tractable—that is, it is easily implemented to compute yield curves. Although it has a constant volatility element, the mean reversion feature removes the certainty of a negative interest rate over the long term. Nevertheless, some practitioners do not favor the model because it is not necessarily arbitrage-free with respect to the prices of actual bonds in the market. 

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