gatheral model of market impact

Gatheral Model of Market Impact

Gatheral proposes the following equation to model market impact dynamics. It is stated using the mathematics of Ito processes.

{% S_t = S_0 + \int_0^t f(x_s) G(t-s) ds + \int_0^t \sigma dW_t %}

Here we have

{% S %} is the price of the asset being traded, which has a constant volatility given by {% \sigma %}.
{% x %} is a trading rate
{% f(x) %} is an instantaneous market impact function
{% G %} is a decay kernel, that is a function that determines how quickly the market impact decays