Asset-backed stable numéraire approach for sustainable valuation

Abstract

ABSTRACT Interest rates underpin almost every instrument/transaction in conventional financial markets. Valuation of the instruments in relation to interest rates remains meaningful only if cash can be attributed a worth of its own (which is generally assumed to accumulate over time). The relevant concepts such as the stochastic short rate and the conventional numéraire (i.e. the money market account) not only become restrictive when one attempts to build more realistic models in quantitative finance, but also – as we demonstrate in this work – their application has de-stabilizing effects on asset valuations. This paper presents a detailed critique of the conventional numéraire and proposes an asset-backed stable numéraire for sustainable valuation of assets and/or transactions. In particular, we demonstrate how some of the key benchmarks of a sustainable footprint may be used as a numéraire currency. We also unveil the implicit assumption underlying the common practice of straightforward factorization in conventional relative pricing to be false.