Abstract
It is natural to assume that interest rates mean-revert, and natural consequence of this is that long forward rates are asymptotically constant. However, from US Treasury STRIPs data, forward rates slope increasingly downwards, and do not attenuate in volatility, as maturity increases beyond about 15 years. We fit an equilibrium model which reconciles this behavior with mean reversion. The key is to extract a latent factor, which the forward rate follows, but overshoots, causing mean reversion on a time scale in terms of weeks. This allows the forward rates to mean revert over the long term in the objective measure but not in the risk neutral measure. We show that this mean reversion can in principle be exploited for profit, and argue that it is not present in the risk neutral dynamic. Our model falls into the Essentially Affine class. We finally set our analysis in the context of similar models for shorter maturities, and discuss applications to managing positions in long maturity bonds and associated derivatives.
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