Vortragsankündigung

Im Rahmen des Kolloquiums spricht

Herr Prof. Dr. Mogens Bladt, 

Department of Mathematical Sciences, University of Copenhagen

über

Modelling of stochastic interest rates

Interest rates play an important role in insurance modelling, particularly in the pricing of longterm insurance products such as life insurance policies. We consider the so-called Markovian interest rate model, where interest rates are assumed to change according to an underlying Markov process. In each state of the Markov process, the spot interest rate is assumed either to be constant or a deterministic function. Either way, the Markovian interest rate models form a dense class of interest models that can approximate any interest rate model. e.g. the oftenused SDE-driven models.

In this talk, we show how to achieve such approximations by linking the Markovian interest rate models to a class of tractable and dense distributions known as phase-type distribution. The link to phase-type theory emerges from the price of a zero–coupon bond being identical to the survival function of a phase-type distribution.

With the phase-type toolbox at hand, we can calibrate a Markovian interest model to observed bond prices or theoretical models, obtain explicit formulas for related quantities such as yield curves and swap rates, and deal with negative interest rates. A number of illustrative examples will be provided.

The Markovian interest rates have the further advantage of integrating particularly well into the so-called multi-state Markov models often used in life insurance modelling (in some countries).

Der Vortrag findet statt am

Mittwoch, den 29.01.2025 um 17.15 Uhr im Raum W01 0-006

Kaffee/Tee um 16.45 Uhr im Raum W1 2-213

Interessierte sind herzlich eingeladen.

Fakultät V

Mathematik und Naturwissenschaften