The evolution of yield curves in 2 factor hull white models

The evolution of yield curves in 2 factor hull white models

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Speaker(s): Ralf Korn (Technische Universität Kaiserslautern), Franziska Diez (Fraunhofer ITWM)

While in simple one-factor models the evolution of the yield curve in time is totally determined by the evolution of the short rate, this is not the case in Hull-White-type multi-factor models. Reasons for this are in particular the initial market forward rate curve as non-controllable input and the multi-factor framework where the current values of the factors are not uniquely determined by the current value of the short rate.

We consider the particular case of the 2-factor-Hull-White model. This is used by the Produktinformationsstelle Altersvorsorge in Germany as the basic ingredient for classifying state-subsidized private pension products in different chance and risk classes. It is thus of particular importance for life insurers when designing products with the aim to belong to a given chance and risk class.

Our main contributions are

  • relations between values of model parameters and the distribution of the frequency of different forms of future yield curves,
  • the effect of the initial market forward rate curve on the future forms of the yield curve and their distributions,
  • intensive numerical studies and examples to highlight practical issues

in the 2-factor-Hull-White model.

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