EL DEPARTAMENTO DE ACTUARÍA Y SEGUROS

Invita al Seminario de Riesgo:

Modelling of stochastic interest rates

Interest rates play an important role in insurance modelling, particularly in the pricing of long-term 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 rate models that can approximate any interest rate model. e.g. the often-used 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, 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 are often used in life insurance modelling (in some countries).

Mogens Bladt
Department of Mathematical Sciences
University of Copenhagen

Jueves, 27 de Febrero de 2025, 13:00
Salón 310, Campus Río Hondo
https://itam.zoom.us/j/98842824361
Meeting ID: 988 4282 4361

El Departamento Académicos de Actuaría y Seguros agradece que extienda esta invitación.