Zero Intelligence (ZI) Trader Model: Parameter Recovery and Uncertainty Using NPE

Table of Links

Abstract and 1. Introduction

2. Relevant Work

3. Methods

3.1 Models

3.2 Summarising Features

3.3 Calibration of Market Model Parameters

4. Experiments

4.1 Zero Intelligence Trader

4.2 Extended Chiarella

4.3 Historical Data

5. Discussion & Future Work

6. Significance, Acknowledgments, and References

4.1 Zero Intelligence Trader

We find that we are able to effectively recover the market simulator parameters using simulation-based inference. Given the posterior, we are able to identify the four parameters with RMSE of 1.85 (+/- 0.52), when using the mid-price and total volume, and RMSE of 1.21 (+/-0.48) when using the VWAP at the fist level of the LOB. These results are shown in Figure 3. We note that the parameter controlling the arrival time for market orders, 𝜇, has a significant uncertainty that spans the prior range and, when using VWAP to estimate posteriors, a distinct bi-modality. This highlights that the ZI model of markets is weakly constrained by arrival time for messages and, furthermore, multiple parameter results may be able to reproduce similar market data.

\ Additional to this, we note that the validation and test loss is reduced when using NSF compared to MAF as the neural density estimator. This is expected, given the bi-modality observed in 𝜇, as NSFs are typically more flexible at reproducing complex distributions. We find that using VWAP data with NSF we are able to reproduce the distinct bimodality in 𝜇 along with being more accurate at predicting the other parameter values. It also indicates that 𝜆, which controls the depth at which orders are submitted, can have a long tail, highlighting the difficulty in determining this parameter value.

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:::info Authors:

(1) Namid R. Stillman, Simudyne Limited, United Kingdom (namid@simudyne.com);

(2) Rory Baggott, Simudyne Limited, United Kingdom (rory@simudyne.com);

(3) Justin Lyon, Simudyne Limited, United Kingdom (justin@simudyne.com);

(4) Jianfei Zhang, Hong Kong Exchanges and Clearing Limited, Hong Kong (jianfeizhang@hkex.com.hk);

(5) Dingqiu Zhu, Hong Kong Exchanges and Clearing Limited, Hong Kong (dingqiuzhu@hkex.com.hk);

(6) Tao Chen, Hong Kong Exchanges and Clearing Limited, Hong Kong (taochen@hkex.com.hk);

(7) Perukrishnen Vytelingum, Simudyne Limited, United Kingdom (krishnen@simudyne.com).

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:::info This paper is available on arxiv under CC BY 4.0 DEED license.

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