Mathematical analysis of different approaches for replicating portfolios

Improving Optimal Terminal Value Replicating Portfolios

“…Motivated by the theoretical results in [7], we improved the cash-flow matching quality of the optimal terminal value portfolio without deterioration of the terminal value match. This is achieved by the introduction of a deterministic strategy (e.g., in replicating assets or risk factors) which approximates the optimal non-deterministic strategy.…”

“…Next, we recall the connection between (RP CF ) and (RPT V ) as established in [7]. If the numéraire asset can be bought or sold at any time, problems (RP CF ) and (RPT V ) are practically the same.…”

“…The following properties of the two optimization problems and their connections were derived in [7].…”

“…For the purpose of improving terminal value matching, we start with the setup as given in [7], that is, we consider the cash-flow matching problem and the terminal value matching problem as proposed in [9] and [8], respectively, and relax the requirement of static replication by allowing for dynamic investment strategies in the numéraire asset. We briefly review the theoretical results derived therein, before we investigate in more detail the benefit of our approach based on market scenarios generated by an insurance company: First, we compare the in-sample and out-ofsample performance of the two replicating portfolios.…”

“…In [7], the two most common approaches, cash-flow matching and terminal value matching, have been investigated from a theoretical perspective and it has been shown that optimal terminal value replicating portfolios are not suitable to replicate liability cash-flows by construction. Thus, their usage for asset liability management is rather restricted, especially for out-of-sample cash profiles of liabilities.…”