Realistic modelling of financial portfolios requires comprehensive models taking all components of the portfolio into account. For instance, not only stock markets have to be modelled, but also the term structure of interest rates (bonds). A common dependence structure should be taken into account.

Members of the Approximity team contributed to the following publications:

  • Risk and performance optimization for portfolios of bonds and stocks Download
    Fischer, T., Roehrl, A.
    Talk at the European Central Bank (ECB), Frankfurt, February 13, 2004
    Slides to explain the accompanying paper: Risk and performance optimization for portfolios of bonds and stocks.
  • Risk and performance optimization for portfolios of bonds and stocks Download
    Fischer, T., Roehrl, A.
    working paper
    We explain how to optimize portfolios of bonds and stocks with respect to the Expected Shortfall (ES), respectively RORC or RORAC based on ES. In a pragmatic approach we combine and correlate a stock market model with geometric brownian motions with a two-factor Cox-Ingersoll-Ross (CIR-2) model for the interest rates/bonds. We use recent results from the theory of risk capital allocation, performance measurement and Swarm Intelligence for optimization. Examples for German market data as well as an analysis of the scalability of the solution to assure fast run-times on clusters of computers for large real-life portfolios are given.
    Approximity sells the accompanying software.
    Online html-version
  • Simulation of the Yield Curve: Checking a Cox-Ingersoll-Ross Model
    Tom Fischer, A. May and B. Walther
    preprint, TU Darmstadt
    We give a complete description of a simulation of future bond prices by a one-factor Cox-Ingersoll-Ross (CIR) interest rate model. Explicit methods and formulas are provided, the time series service of the German Federal Reserve is used as data source. Several model checks are developed and applied to the CIR model. As a result, the model has to be rejected for the German debt securities market.
  • Anpassung eines CIR-k-Modells mit Hilfe der Kalman-Filter-Methode
    Tom Fischer, Angelika May, Brigitte Walther
    preprint, TU Darmstadt
    (German article for practitioners in German life insurance companies). In dieser Arbeit wird erlaeutert, wie die Theorie des Kalman-Filters fuer die Parameterschaetzung eines Cox-Ingersoll-Ross-Models mit k Faktoren genutzt werden kann. Die zunaechst theoretische Ausfuehrung der Vorgehensweise wird an Hand des Deutschen Rentenmarkts konkretisiert.

market and term structure modelling specialist

back to top