Analysis of popular replicating portfolio approaches Seminar

We consider the most popular approaches for the construction of replicating portfolios for life insurance liabilities known as cash flow matching and terminal value matching. Solutions to these problems are derived analytically and a detailed comparison is provided. It is shown that the (unique) solutions have fair value equal to the fair value of liabilities. Then, the problems are generalized by relaxing the requirement of static replication to allow for dynamic investment strategies in a numeraire asset with zero present value. A relationship between the solutions to these generalized problems is established, which sheds new light on the relation of the original problems. Finally, it is proved that the fair values of the optimal solutions to the generalized problems remain equal to the fair value of liabilities. Based on numerical examples it is shown that the dynamic investment strategies can be reasonably approximated by linear regression, such that an out-of-sample implementation, as e.g. needed for MCEV and Solvency II calculations, is possible.

Co-authors: This is joint work with Jan Natolski (Augsburg University)