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Quantitative Finance · Glossary

What is Propagator model, decay kernel?

Also known as: propagator model · decay kernel

Definition 12.1 Microstructure and Execution · Chapter 12 — Transient Impact and Propagator Models

The propagator model writes the price before trade tt as the sum of the impacts of all past trades,

pt=∑s<tG(t−s) εs+noise,p_t=\sum_{s<t}G(t-s)\,\varepsilon_s+\text{noise},

where the decay kernel (the propagator) G(ℓ)G(\ell) is the impact of one trade ℓ\ell trades later, independent of the others.

The propagator fitted on two simulated hours. Left: the sign autocorrelation (long memory) and the fitted kernel (slow decay). Right: the variance of price changes per lag: flat means diffusive. Data: mx_prop.kernel_study.
Figure 12.1. The propagator fitted on two simulated hours. Left: the sign autocorrelation (long memory) and the fitted kernel (slow decay). Right: the variance of price changes per lag: flat means diffusive. Data: mx_prop.kernel_study.
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