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.

@en

In times of market turmoil volatility increases and stock values and interest rates decrease, so that the risks in the balance sheets of insurance companies increase. An important part of these risks is due to the guarantees that are embedded in insurance policies. Life insurers sell products like unit-linked, profit sharing and variable annuity products. These contracts contain guarantees to the policyholders. Such contracts embedded in the insurers’ liabilities are called embedded options. The value and cash flow of these contracts are respectively relevant for the balance sheet and the profit and loss account. Typically in periods of volatile markets, the value of these embedded options increase, so that the insurance company must hold a larger liability value on the balance sheet in order to be able to pay out future cash flows. The valuation of these embedded options in insurance liabilities is therefore important to insurers for risk management applications. In this thesis we consider various topics regarding the valuation of these embedded options.@en