School of Mathematical and Physical Sciences, University of Technology, Sydney

Benchmark Approach to Finance

This lecture introduces into the benchmark approach that provides a general framework for financial modelling by employing the numeraire portfolio as benchmark and numeraire. It provides a unified treatment of portfolio optimization, derivative pricing and risk management. A diversification theorem allows forming a proxy for the numeraire portfolio. The benchmark approach extends the classical asset pricing theories, opening new possibilities for long term risk management, relevant to e.g. pensions, insurance, financial planning and regulation. The real world price is characterising the minimal possible price, below those of other pricing rules. The richer modelling framework of the benchmark approach leads naturally to tractable, realistic long term models. It will be explained how the approach differs from the classical risk neutral approach. Examples on long term and extreme maturity derivatives demonstrate how long dated contracts can be less expensively priced and hedged than suggested by classical theory.