Thin Trading and the Singularity Spectrum: Evidence from Tokenized Carbon Markets

Spectral width, the standard multifractal measure of market complexity, is established for actively traded sustainable assets such as carbon allowances and green bonds. Tokenized green assets trade thinly, and we calibrate how far the measure can be trusted, using KlimaDAO’s carbon tokens, whose prices we rebuild from on-chain swaps so that inactivity is observed rather than inferred. Four problems appear. Filling empty intervals with the last price widens the spectrum when the market is unchanged, and the part driven by large fluctuations less so. A test on overlapping rolling windows reports differences that are not there too often. Aggregator prices make the carbon tokens look more different than their own trades show. And the execution price of a swap, which carries the fee, narrows the spectrum of a deep pool. Under these controls the four carbon tokens have wider spectra than wrapped Bitcoin and Ether rebuilt from the same exchanges, a difference so few units cannot establish at conventional levels, and no wider than conventional tokens that trade as thinly. Among conventional tokens, width falls with the market capitalisation of the asset. Whether the pools’ quality tiers differ remains undetermined, since no two tiers were liquid over the same period.