We extend a Discrete Time Random Walk (DTRW) numerical scheme to simulate the anomalous diffusion of financial market orders in a simulated order book. Here using random walks with Sibuya waiting times to include a time-dependent stochastic forcing function with non-uniformly sampled times between order book events in the setting of fractional diffusion. This models the fluid limit of an order book by modelling the continuous arrival, cancellation and diffusion of orders in the presence of information shocks. We study the impulse response and stylised facts of orders undergoing anomalous diffusion for different forcing functions and model parameters. Concretely, we demonstrate the price impact for flash limit-orders and market orders and show how the numerical method generate kinks in the price impact. We use cubic spline interpolation to generate smoothed price impact curves. The work promotes the use of non-uniform sampling in the presence of diffusive dynamics as the preferred simulation method.

翻译：我们将离散时间随机游走（DTRW）数值方案扩展到模拟订单簿中金融市场订单的异常扩散。这里采用具有Sibuya等待时间的随机游走，在分数扩散的框架下引入随时间变化的随机强迫函数，并对订单簿事件间非均匀采样时间进行建模。通过模拟信息冲击下订单的连续到达、撤销与扩散过程，该模型刻画了订单簿的流体极限。我们研究了不同强迫函数与模型参数下经历异常扩散的订单的脉冲响应及典型事实。具体而言，我们展示了闪电限价单和市价单的价格影响，并揭示了数值方法如何在价格影响中生成拐点。采用三次样条插值法生成平滑的价格影响曲线。本工作提倡在存在扩散动力学的情况下，将非均匀采样作为优选模拟方法。