Cash Flow Replication with Mismatch Constraints

The replication of a portfolio of cashflow instruments with another set of cashflow instruments is frequently used for pricing and hedging. For example, replication of deposits with tradable bonds allows the treasurer to determine an approximate fair value of deposits and implement hedging schemes. In these applications the replication of deposits with tradable instruments is crucial as this re-states the problem of pricing and hedging deposits into, for the treasury trader well-known, standard market instrument valuation and hedging. In an insurance context replicating portfolio is also used to replace non-tradable policies such as life annuities with a best hedging tradable cashflow portfolio. In the application of replicating portfolio a key issue is what asset instruments should be used for replication in order to achieve a minimal cashflow deviation. Having determined the set of assets to use in replication the next key step is to determine a model for replication error measurement and other features of the replicating portfolio such as the cost. In this paper we describe an efficient linear program approach to cashflow replication. This program explicitly controls the replication error as mismatch constraints with user defined tolerance levels for absolute and tail mismatch. By controlling the cashflow mismatch as constraints the non-feasibility of any given asset portfolio simply indicates a bad choice of replicating instruments, or, a bad choice of constraints. For feasible problems the linear optimization finds the minimum cost portfolio of the feasible set. The cashflow optimization approach with cashflow mismatch as constraints has significant advantages over naive approaches to cashflow replication that directly minimize the cashflow deviation between the portfolios.