Radial basis functions for option pricing in insurance liabilities

This thesis discusses the valuation of embedded options in insurance liabilities using radial basis functions. For insurance companies, the valuation of embedded options is an important topic within risk management. This valuation can become too computationally heavy when nested Monte Carlo simulations are used. To overcome this computational drawback, this thesis proposes an alternative method: the construction of an interpolation function based on radial basis functions. An overview of the interpolation method is presented, along with detailed looks into its features, exploring the topics accuracy, numerical stability, calibration of parameters and extrapolation. Furthermore, a new technique to sample data centers is presented. Starting with a small initial data set, new data centers are sampled iteratively. By doing so, in each iteration the current interpolation can be assessed; new data centers are based on this assessment. The use of such a data-dependent bottom-up sampling procedure is motivated by the computational costs related to constructing data centers; the number of data centers is preferably as low as possible.

Subject

numerical
interpolation
radial basis function
option pricing

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Student theses

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master thesis

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Thesis_Eric_Schols.pdf

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