Cashflow replication with mismatch constraints

Wei Chen and Jimmy Skoglund

Abstract

ABSTRACT

The replication of a portfolio of cashflow instruments with another set of cashflow instruments is frequently used in pricing and hedging. For example, replicating deposits with tradable bonds allows the treasurer to determine an approximate fair value of deposits and to implement hedging schemes. In these applications, the replication of deposits with tradable instruments is crucial, as this restates the problem of pricing and hedging deposits as a standard problem of market instrument valuation and hedging. In an insurance context, a replicating portfolio is also used to replace nontradable policies, such as life annuities, with a best-hedging tradable cashflow portfolio. Again, the transformation of nontradable balance sheet items into replicating tradable instruments allows hedging schemes and other forms of analysis, such as asset and liability management, to be implemented with respect to the market-traded replicating portfolio. When applying a 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 for 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 using mismatch constraints with user-defined tolerance levels for absolute and tail mismatch. By controlling the cashflow mismatch using constraints, the nonfeasibility 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 minimal-cost portfolio of the feasible set. The cashflow optimization approach with cashflow mismatch constraints has significant advantages over naive approaches to cashflow replication that directly minimize the cashflow deviation between the portfolios.