Greenvexity: Explicitizing green bonds’ implicit optionality

Given green bonds’ observed convexity, attributed principally to their asymmetric liquidity, we seek to explicitly value European spread options on the excess returns of green bond risky spread versus that of conventional comparators. This provides a new perspective for evaluating relative green bond pricing ex ante and serves to partially justify their commonly perceived pricing premium, or “greenium”. Since greenium variation can be reasonably emulated by a univariate Gaussian mixture model, the closed-form Bachelier model can be modified to efficiently price options on the excess return of green risky spreads, in spread terms. We additionally explore the wide-ranging utility of the introduction of such nonlinear derivatives in practice.