Conditional Fat Tails and Scale Dynamics for Intraday Discrete Price Changes

We investigate the conditional tail behaviour of asset price changes at high (10-second) frequencies using a new dynamic model for integer-valued tickdata. The model has fat tails, scale dynamics, and allows for possible over- or under-representation of zero price changes. The model can be easily estimated using standard maximum likelihood methods and accommodates both polynomially (fat) and geometrically declining tails. In an application to stock, cryptocurrency and foreign exchange markets during the COVID-19 crisis, we find that conditional fat-tailedness is empirically important for many assets, even at such high frequencies. The new model outperforms the thin-tailed (zero-initiated) dynamic benchmark Skellam model by a wide margin, both insample and out-of-sample.