Approximation of insurance liability contracts using radial basis functions

ABSTRACT

We introduce the Option Interpolation Model (OIM) for accurate approximation of embedded option values in insurance liabilities. Accurate approximation is required for ex-ante risk management applications. The OIM is based on interpolation with radial basis functions, which can interpolate scattered data, and does not suffer from the curse of dimensionality. To reduce computation time we present an inversion method to determine the interpolation function weights. The robustness, accuracy and efficiency of the OIM are investigated in several numerical experiments. We show that the OIM results in highly accurate approximations.

KEYWORDS:

• Radial basis function
• nested simulation
• solvency II
• insurance

2010 JEL CLASSIFICATIONS:

• C02
• C10
• C13
• C52
• C53
• C58
• C63
• C80
• G12
• G13
• G17
• G22
• G23
• G29

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 This depends generally on the definition of the RBF.

2 The behaviour of the data-dependent shape parameter is similar as for the data-independent shape parameter.

3 Equation (30(30) $w=U^{-1}u\mathrm{where}u=L^{-1}y.$(30) ) contains inverses, though in practice these inverses are never computed explicitly, as solving the whole system is more accurate and faster than explicitly computing the inverse, as is well-known.

4 Unit-Linked product are guaranteed investment return products.