A Formalized Hybrid Portfolio Replication Technique Applied to Participating Life Insurance Portfolios

Abstract

The practice of portfolio replication has proven its applicability to market risk management in complete markets through the appropriate modeling of a range of non-linear financial instruments. Replicating portfolios provide an intuitive and operational framework for explaining financial risks of life insurance companies as financial instruments with analytical formula encompassing instruments’ non-linearities, path dependency and specific sensitivities capture financial risks. Carrying out the market risk calculation for life insurance companies requires the replicating portfolio technique as the plan calculation referred to as ‘stochastic in stochastic’ requires immense computational power. For each of the real-world scenarios, the market-consistent values of assets and liabilities on the basis of the replicating portfolio technique are therefore determined. This article presents an enhanced replicating portfolio framework that is of utmost importance for the generation of market risk capital requirements applied to life insurance portfolios embedding options and guarantees. While the classic replication technique requires approximations and expert judgments as there is no clear-cut, easy answer for finding an optimal replicating portfolio providing a superior replication power (i.e. a portfolio composed of a finite number of financial vanilla instruments in an arbitrage-free context out of which the cash-flows best replicate the magnitude and timing of liabilities over the projection term), the proposed approach relies on a formalized framework that leads to build optimal replicating portfolios for participating life insurance business. This paper derives the principles behind the portfolio replication technique and provides explanations and justifications on the parameterization of replicating portfolios via a practical application case. The approach adopted is a hybrid model that combines a 'pure' portfolio replication technique and the curve fitting approach. As a result, the quality of replicating portfolios in extreme capital market environments is tested by means of a comparison with the results of a brute force revaluation incorporating a large range of sensitivities such as EEV, QIS 5 and extreme scenario (close to the economic capital driven scenario) sensitivities. In order to determine the weights of financial instruments, the ordinary least square technique is used to find the best possible portfolio composition that replicates liability cash flows in several market conditions at either the present or terminal value of the projection. Additional enhancement techniques such as a particular adjustment within the singular value decomposition and a scenario filter are introduced to better fit the weights of selected instruments with liability moves. An example of calibration strategy that leads to an optimal replicating portfolio is broadly described in this paper.