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5th Meeting of the Freiburg-Strasbourg research group

With presentations of Stefan Tappe and Thomas Krabichler

When Oct 02, 2018
from 10:00 AM to 12:00 PM
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10.00 Stefan Tappe, University Freiburg 
Stochastic mortality and interest rates: An infinite dimensional approach
11.00 Thomas Krabichler   
A Joint Modelling Framework for Credit and Liquidity Risk
FRIAS, Alberstr. 9, 79104 Freiburg, 
Großer Seminarraum
Abstract S. Tappe 
This presentation aims to discuss a joint framework for mortality and interest rates, and it is divided into three parts:
1) First we present a model for the so-called forward mortality rates, which are a measure for the danger of death up to a specified time for individuals of a population. We show that the mortality rates have to satisfy certain consistency conditions, and we translate their dynamics into a stochastic partial differential equation (SPDE) for the mortality rates.
2) Then we review Heath-Jarrow-Morton (HJM) type forward rate models in the spirit of the Benchmark Approach, and we also derive a SPDE for the interest rates.
3) Note that we have formulated both SPDEs under the real-world probability measure P. In the last step, we bring these two approaches together and suggest a unified SPDE for mortality rates and interest rates.
Abstract T. Krabichler
We consider an arbitrage-free financial market with zero-coupon bonds that are exposed to credit and liquidity risk. We revisit the famous Jarrow \& Turnbull setting in order to account for these two intricately intertwined risk types. We provide an example of tractable term structure models that are driven by a two-dimensional affine jump diffusion. Furthermore, we derive explicit valuation formulae for marketable products.
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