Replicating portfolios revisited

Many market leaders in the insurance industry use stochastic projections for their risk-based capital (RBC) calculations instead of using a standard formulaic way to calculate the RBC. Deriving the market value of liabilities in a case where the liabilities have options and guarantees embedded, one has to use a market-consistent, risk-neutral valuation. However, this calculation is rather complex and, when performed in a straightforward manner, involves running a cash-flow projection model under a large number of risk-neutral scenarios. Even if the computation of the liabilities’ market value for a single scenario is relatively fast, one can quickly incur very large processing and calculation costs, as this single computation needs to be repeated tens of thousands times.

This research report introduces two methods allowing for a robust and reliable calibration of replicating portfolios: 1) the use of orthogonal calibration scenarios and 2) the use of principal component analysis of the candidate assets in combination with a criteria-based model selection procedure. The authors recommend the use of orthogonal calibration scenarios together with principal component analysis of the candidate assets when calibrating a replicating portfolio.