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Modelling bid-ask spread conditional distributions using hierarchical correlation reconstruction

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  • Jaros{l}aw Duda
  • Robert Syrek
  • Henryk Gurgul

Abstract

While we would like to predict exact values, available incomplete information is rarely sufficient - usually allowing only to predict conditional probability distributions. This article discusses hierarchical correlation reconstruction (HCR) methodology for such prediction on example of usually unavailable bid-ask spreads, predicted from more accessible data like closing price, volume, high/low price, returns. In HCR methodology we first normalize marginal distributions to nearly uniform like in copula theory. Then we model (joint) densities as linear combinations of orthonormal polynomials, getting its decomposition into (mixed) moments. Then here we model each moment (separately) of predicted variable as a linear combination of mixed moments of known variables using least squares linear regression - getting accurate description with interpretable coefficients describing linear relations between moments. Combining such predicted moments we get predicted density as a polynomial, for which we can e.g. calculate expected value, but also variance to evaluate uncertainty of such prediction, or we can use the entire distribution e.g. for more accurate further calculations or generating random values. There were performed 10-fold cross-validation log-likelihood tests for 22 DAX companies, leading to very accurate predictions, especially when using individual models for each company as there were found large differences between their behaviors. Additional advantage of the discussed methodology is being computationally inexpensive, finding and evaluation a model with hundreds of parameters and thousands of data points takes a second on a laptop.

Suggested Citation

  • Jaros{l}aw Duda & Robert Syrek & Henryk Gurgul, 2019. "Modelling bid-ask spread conditional distributions using hierarchical correlation reconstruction," Papers 1911.02361, arXiv.org.
  • Handle: RePEc:arx:papers:1911.02361
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    References listed on IDEAS

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    1. Mestel, Roland & Murg, Michael & Theissen, Erik, 2018. "Algorithmic trading and liquidity: Long term evidence from Austria," Finance Research Letters, Elsevier, vol. 26(C), pages 198-203.
    2. Chen, Xiaohong & Linton, Oliver & Yi, Yanping, 2017. "Semiparametric identification of the bid–ask spread in extended Roll models," Journal of Econometrics, Elsevier, vol. 200(2), pages 312-325.
    3. Henryk Gurgul & Artur Machno, 2017. "The impact of asynchronous trading on Epps effect on Warsaw Stock Exchange," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 25(2), pages 287-301, June.
    4. Farshid Abdi & Angelo Ranaldo, 2017. "A Simple Estimation of Bid-Ask Spreads from Daily Close, High, and Low Prices," Review of Financial Studies, Society for Financial Studies, vol. 30(12), pages 4437-4480.
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