The Value of Convexity: A Theoretical and Empirical Investigation
33 Pages Posted: 2 Sep 2015
Date Written: September 1, 2015
We explore from a theoretical and an empirical perspective the value of convexity in the US Treasury market. We present a quasi-model-agnostic approach that is rooted in the existence of some affine model capable of recovering with good accuracy the market yield curve and covariance matrix. As we show, at least one such model exists, and this is all we require for our results to hold. The model does not have to be specified or calibrated (its parameters determined statistically). It is in this sense that we call our approach 'quasi-model-agnostic'.
We present empirical results about the predictive power of this approach. By looking at 30 years of data, we find that neither the strategy of being systematically long or short convexity (and immunized against 'level' and 'slope' risk) would have been profitable. However, a conditional strategy that looks at the difference between the 'implied' and the statistically estimated volatilities would have identified extended periods during which the convexity was not correctly priced (by which we mean that it was possible to make money by being long or short convexity as our approach suggests, while remaining hedged against the yield curve factors).
Keywords: yield curve modelling, affine models, convexity
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