A Deeper Look: Parameter Calibration in a Complex Market Model (Extended Chiarella)

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

4.2 Extended Chiarella

We find that we are also able to identify the parameters for the extended Chiarella model. This is significant, as this model is more complex with an increase in the number of parameters and with greater flexibility in the overall output of the simulator. We find that we are able to calibrate the 6 parameters with a RMSE of 0.77 (+/- 0.26) when using the midprice and total volume data and RMSE of 0.82 (+/- 0.29) when using the VWAP at the first level. While the overall accuracy slightly decreases when using VWAP, we find that the overall uncertainty reduces around those parameters where the posterior probability distribution is already constrained, such as 𝜎𝑁, 𝛽ℎ 𝑓 and 𝜅. This indicates a tradeoff on whether the single point estimate for the parameter values is used or the explicit posterior is of interest for example, to evaluate model drift as we discuss in section 5. Moreover, examination of the posterior distribution for specific parameters gives additional insight into model assumptions.

\ We observed two interesting features in the estimated posterior probability distribution for the extended Chiarella model. First, as discussed above, we find that a subset of parameters have low variance, such that uncertainty is reduced. These are the parameters controlling the noise traders and the fundamental traders, 𝜎𝑁 and 𝜅. However, for momentum traders, we are able to calibrate the decay term for both high frequency and medium frequency parameters, 𝛽 and 𝛽ℎ 𝑓 with low uncertainty. In general, we find that the parameters that control this trader behaviour typically have uncertainties that span the prior. We discuss the implications for this in section 5.

\ We note that we were unable to achieve good test performance when using NSFs and were required instead to use MAFs. This may be due to the increased dimension in parameter space, which caused the neural network to over-fit. We trialed different initial learning and dropout rates but observed significant divergence between training and validation loss during training time. Given that MAFs are typically more expressive than NSFs, and are able to capture more complex dependencies between variables, this may be due to the increased dimensionality of the size of the parameter set. As such, we may need a larger simulation budget in order to better estimate the distribution. Future work will investigate this further.

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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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