A third order factor for immunization: Implications into Solvency II

A third order factor for immunization: Implications into Solvency II

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Speaker(s): J. Iñaki De La Peña (University of the Basque Country (UPV/EHU))

Usually, when Immunization is used in the insurance companies , the investment strategy contemplates the first and second order of Taylor's development (Duration and Convexity). It is well known that strategies using both parameters do not annul the risk of interest - positive matching and/or horizon matching-. In Absolute matching strategy, however, there is no problem if bonds are used until their maturity. In this case, interest risk does not exist because the strategy developed is a dedicated fund one.

Nevertheless, if more parameters of Taylor's development are included, the result of the strategy changes. Though a model can be contemplated for s-orders into the Taylor´s development, this study is realized for the special case of s=3.

The aim of this paper is to analyze the effects of the third term of Taylor's development into an immunization strategy, in order to liberate the part of the capital requirement for the Solvency of the insurance firm due to interest risk. The risk of the model is born, precisely of the difference between the real value and the estimated one via duration and convexity approximation (second order). Therefore, the skewness and, consequently, the fitness of the model are analysed upon second and third order approximation, taken into account that in the same equation there are equivalent values for the liabilities (expected Duration, expected Convexity and the expected third order). With these values, a specific minimax strategy that reduces this influence in a given horizon of time is established.

One of the conclusions is that the immunized portfolio with three factors necessarily matches duration and convexity and, in addition, with the third order development the capital requirement for solvency inside SCR's corresponding module is lower.

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