Damir Filipovic

Swiss Finance Institute, Ecole Polytechnique Federale de Lausanne, Switzerland

Variance Swap Rate Factor Models

Abstract: In this talk, I present some novel parametrization for affine variance swap rate factor models, which can also be applied for interest rate futures. First, we observe that an affine variance swap term structure implies that the drift of the state process is necessarily affine, while its martingale part can be chosen arbitrary. This allows for great statistical flexibility, and is in contrast to affine interest rate models, where also the martingale characteristics of the state process are necessarily affine. We then discuss a drift parametrization with m+1 degrees of freedom which asserts that the components of the m-dimensional state process can be matched with m pre-specified points on the term structure. This will greatly facilitate the empirical estimation for such stochastic models. Moreover, sufficient and yet flexible conditions that guarantee positivity of the rates are readily available. We finally discuss the relation and differences to affine yield-factor models introduced by Duffie and Kan (1996). Indeed, in contrast to variance swap models, their yield factor representation requires imposing constraints on systems of nonlinear equations that are often not solvable in closed form.