Random trade timing and power-law tails in realized prices

TL;DR

This paper demonstrates that random trade timing and trading heterogeneity can produce power-law tails in realized prices, even when the underlying latent price process is light-tailed.

Contribution

It introduces models showing how random trade timing mechanisms generate Pareto-type tails in realized prices from light-tailed latent processes.

Findings

Random trade timing can produce Pareto tails in realized prices.

Tail exponent depends on the least frequent trading type.

Heterogeneity in trading affects the scale constant of tails.

Abstract

This paper studies stochastic mechanisms under which light-tailed latent price dynamics yield realized prices with power-law tails. The realized price is modeled as $P_T=e^{X_T}$, where $X$ is a Markov-modulated L\'evy process and $T$ is the random time of the next trade. We consider two trade-timing environments. In the intertrade-incidence model, trades occur on a discrete grid with type-dependent probabilities. In the intertrade-time model, the waiting time to the next trade is generalized Erlang, allowing for heterogeneous arrival rates and transaction-completion delays. We show that random trade timing can generate Pareto-type tails, possibly with a logarithmic correction, in realized prices even when the latent price process is light-tailed. In both models, the tail exponent is determined by the least frequent trading type, while the proportions of faster-trading types affect only the scale constant. We also provide sufficient conditions under which these Pareto-type tails sharpen to exact Paretian tails. These results identify random trade timing and heterogeneity in trading behavior as a general mechanism for generating power-law tails in realized prices.