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Bright squeezed vacuum (BSV), the radiation at the output of a strongly pumped unseeded parametric amplifier, is known to have strong and fast intensity fluctuations. This makes it more efficient than coherent light for pumping multiphoton effects. Recently we have demonstrated this feature for non-phasematched 2nd-4th harmonic generation. In particular, for the 4th harmonic generation, BSV is two orders of magnitude more efficient than coherent light with the same pulse duration and energy per pulse. The resulting radiation of optical harmonics has even stronger intensity fluctuations than BSV and manifest giant superbunching. Their photon-number distributions are heavy-tailed and resemble the statistics of ‘rogue waves’ in the ocean and their analogues in nonlinear optics. For optical supercontinuum generated from BSV, we observe even more drastic ‘rogue-wave’ behaviour, featuring a power-law (Pareto-type) probability distribution of photon number. The power exponent of this distribution is less than two, meaning that even the mean photon number is indefinite, to say nothing of higher moments. The highest bunching parameter we observed was 170, but its value is, in principle, unlimited because the second moment of the photon number diverges. This extreme superbunching has interesting consequences for photon subtraction experiments, which we indeed performed with supercontinuum produced from BSV. As a result of photon subtraction, the mean photon number increased by two orders of magnitude. From the viewpoint of quantum thermodynamics, this means that a large amount of thermodynamical work can be extracted from this state of light.