In this part of the book we look again at convexity. We want to understand if the value of convexity is fairly reflected in the shape of the yield curve. This means that we must first estimate what convexity ‘should be’ and then compare our theoretical estimates with the market's.

We carry out this comparison from three different angles.

The first (Chapter 20) is model driven, in the sense that we look at the output from affine models to gauge the value of convexity.

The second (dealt with in Chapter 21) is (almost) model agnostic, and looks at what the shape of the yield curve (its ‘carry’ and its ‘roll-down’) tells us about what the value of convexity should be.

The third (Chapter 22) is empirical: given what we have learnt about what convexity should be, we explore whether any discrepancies between the theoretical and the observed curvature of the yield curve can be effectively exploited.

As we shall see, extracting the value of convexity boils down to crystallizing the difference between what yield volatilities should be in theory and what they will be in practice. The infinitely wise words of Yogi Berra's that provide the opening quote to Chapter 22 act as a healthy reminder of the width of the chasm that, more often than not, separates theory and reality.