Orateur
Dr
Zorana Grbac
(Université Paris Diderot)
Description
The class of polynomial preserving Markov processes has proved to be very suitable for modeling purposes in mathematical finance due to its flexibility and analytical tractability, which allows to obtain closed/semi-closed pricing formulas for various derivatives. In this work we focus on an application of this class for interest rate models on a discrete tenor. Here the polynomial preserving property of the driving process is key already in the model construction which is based on polynomial functions. This includes Libor-type models, as well as extensions to the multiple-curve term structure. The main advantage of this model class is the possibility to obtain at the same time semi-analytic pricing formulas for both caplets and swaptions that do not require any approximations. Moreover, additive constructions allow to easily ensure, if desired, properties such as positivity of interest rates and spreads and monotonicity of spreads with respect to the tenor - in view of the current market situation a model in which the reference OIS interest rates can become negative and the spreads still remain positive is of particular interest.
We conclude by presenting a model specification driven by a Lévy-type polynomial preserving process and a corresponding Fourier transform formula used in pricing of caplets and swaptions.
This is joint work with K. Glau and M. Keller-Ressel.
Auteur principal
Dr
Zorana Grbac
(Université Paris Diderot)
