Historical Data

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

4.3 Historical Data

Having demonstrated that we are able to calibrate synthetic data using neural density estimators and embedding networks, we next use our calibration procedure to identify model parameters specific to a single day of trading. We use data from the Hong Kong exchange (HKEX) which reflects a standard trading day. We first evaluate the stylised facts on the historical data to see which are supported and which are violated. As shown in Figure 2, we see that (a) log returns follow a typical normal distribution at medium timescales (minutes) but that this departs from normality as we shorten the timescale (seconds), resulting an increase in kurtosis. Additionally, when calculating the skewness at both timescales, we observe a slight asymmetry (0.44).

Shown in Figure 2(c), we observe an absence of autocorrelation in the return series, in (d), a positive correlation between volume and volatility and in (e) we see significant volatility clustering at high lag number. We also observe intermittency in historical data, a large Hurst exponent (0.8) and that the autocorrelation of absolute returns rapidly converges to zero reflecting that the historical data has no long range memory or dependencies, and the order book volumes approximate a Gamma distribution, where 𝛾 = 0.014, 0.018 for bid and ask orders, respectively. However, we also note that some stylised facts are not observed in this data, such as a negative correlation between returns and volatility, and significant concavity in the price impact function, which is essentially flat at 0.07.

In Figure 4, we show the estimated posterior distribution for the historical data using the VWAP from the fist level of the LOB. We again observe that parameters for the fundamental trader and noise trader are constrained, whereas those for the momentum trader have high uncertainty. Interestingly, we see that the decay rate for high frequency traders has reduced uncertainty, indicating that high frequency behaviours may be significant in this trading day. Future work will investigate this. Shown in Figure 2, we are again able to reproduce several of the stylised facts, including (a) the heavy tails and normality of log returns, (c) the absence of auto-correlations in return series, and (e) a strong correlation between volume and volatility, as well as intermittency, no long range memory (where the Hurst exponent is 0.76) or dependencies of absolute returns, and a Gamma distribution in the order book volume (where 𝛾 = 0.28 for both bid and ask orders). Interestingly, we observe that our simulator is able to recreate stylised facts that are not present in the historical data such as negative correlation between returns and volatility and a stronger asymmetry in returns (-0.95). We again observe that the price impact function is approximately flat (0.01). The only stylised fact that is observed less strongly in our simulator is the volatility clustering, shown in Figure 2(f), which decreases with increasing lag but is not consistently positive.

We next use the historical data to estimate the posterior for the ZI trader model, as shown in Figure 5. We find that the parameter values are constrained with similar uncertainties as observed when using synthetic data. We again see a sharp bi-modality in the rate at which market orders are submitted that spans the prior. When calculating the stylised facts, we observe the same behaviours as with the extended Chiarella model. However, the price impact function is now convex (with coefficient -0.25) and where there is negligible correlation between returns and volatility (correlation coefficient is -0.0005).