Measurement of solvency capital requirement for the interest rate risk using the Standard Formula: a stochastic model to evaluate a participating life insurance contract

The interest rate risk is relevant in the creation of a life insurance company’s solvency capital requirement. In the article we address the problem of its measurement when the company has with-profit insurance contracts with a minimum guaranteed rate in its portfolio and uses the Standard Formula. A stochastic model and the Monte Carlo simulation is needed to calculate the technical provision. We propose a Cox-Ingersoll-Ross model with an exogenous barrier extended with a deterministic function which allows to estimate negative rates and the perfect-fit of the term structure of interest rates, measured using the Smith-Wilson method. We also introduce an alternative method to define the upward and downward scenarios which is consistent with the regulatory framework.