The practice of portfolio replication. A practical overview of forward and inverse problems

Portfolio replication is a powerful tool that has proven in practice its applicability to enterprise-wide risk problems such as static hedging in complete and incomplete markets and markets that gap; strategic asset and capital allocation; benchmark tracking; design of synthetic products; and portfolio compression. In this paper, we revise the basic principles behind this methodology, currently used by financial institutions worldwide, and present several practical examples of its application. We further show how inverse problems in finance can be naturally formulated in this framework. In contrast to mean-variance optimization, the scenario approach allows for general non-normal, discrete and subjective distributions, as well as for the accurate modeling of the full range of nonlinear instruments, such as options. It also provides an intuitive, operational framework for explaining basic financial theory.