Department of Economics and Business Economics

An analysis of a three-factor model proposed by the Danish Society of Actuaries for forecasting and risk analysis

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This paper provides the explicit solution to the three-factor diffusion model recently proposed by the Danish Society of Actuaries to the Danish industry of life insurance and pensions. The solution is obtained by use of the known general solution to multidimensional linear stochastic differential equation systems. With offset in the explicit solution, we establish the conditional distribution of the future state variables which allows for exact simulation. Using exact simulation, we illustrate how simulation of the system can be improved compared to a standard Euler scheme. In order to analyze the effect of choosing the exact simulation scheme over the traditional Euler approximation scheme frequently applied by practitioners, we carry out a simulation study. We show that due to its recursive nature, the Euler scheme becomes computationally expensive as it requires a small step size in order to minimize discretization errors. Using our exact simulation scheme, one
is able to cut these computational costs significantly and obtain even better forecasts. As probability density tail behavior is key to expected investment portfolio performance, we further conduct a risk analysis in which we compare well-known risk measures under both schemes. Finally, we conduct a sensitivity analysis and find that the relative performance of the two schemes depends on the chosen model parameter estimates.
Original languageEnglish
JournalScandinavian Actuarial Journal
Pages (from-to)837-857
Number of pages21
Publication statusPublished - 2016

    Research areas

  • Monte Carlo simulation, Exact simulation, Multi-factor diffusion model, Forecasting, Risk analysis, Local sensitivity analysis

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