Seminario: Discrete-tenor interest rate models based on polynomial preserving processes

Venerdì 24 Aprile 2015, ore 9:00 - Aula 1BC45 - Zorana Grbac


Venerdì 24 Aprile 2015 alle ore 9:00 in Aula 1BC45, Zorana Grbac terrà un seminario dal titolo "Discrete-tenor interest rate models based on polynomial preserving processes".

Based on the class of polynomial preserving Markov processes, we construct families of positive martingales, which are monotone with respect to some parameter. Such martingales are particularly suitable for modeling of discretely compounded forward interest rates via additive constructions. 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 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. Examples of tractable and flexible model specifications that we study include quadratic OU-Gaussian and OU-L?vy processes, as well as linear models. We discuss the efficient option pricing via Fourier methods and develop the necessary exponential transform formulas for polynomial preserving processes.
This is joint work with K. Glau and M. Keller-Ressel.