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
mdimensional state process can be matched with m prespecified 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
yieldfactor 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.
