Predicting Intraday Price Distributions at High Frequencies

50 Pages Posted: 16 Jul 2013 Last revised: 9 Aug 2013

Matti Antola

Valo Research and Trading

Tommi A. Vuorenmaa

Triangle Intelligence

Date Written: August 9, 2013


We propose extensions to the continuous-time random walk (CTRW) framework so far mainly developed within the econophysics community. Using numerical methods, we extend the CTRW framework with more general marginal distributions than previously proposed. There are two main findings in this respect: First, modeling the returns with a Student-t distribution gives at least as good price distribution predictions as the other previously proposed distributions in this framework. Second, a mixed-Weibull waiting time distribution fits exceptionally well to our three-week long Nasdaq OMX data. When combined with standard financial econometric GARCH and ACD models and intraday seasonality filtering procedures new to the CTRW framework, our models deliver realistic intraday Value-at-Risk and Expected Shortfall predictions. Compared to the basic CTRW model, the total average performance improvement is typically around 70 percent. The effect of filtering out memory in waiting times is particularly noticeable: around 50 percent of the total performance improvement. Overall, our extensions and filtering methods make the CTRW framework a useful tool for intraday risk management (trading), especially at high frequencies of less than a minute or so.

Keywords: Continuous-time random walk, high-frequency data, intraday prediction, Value-at-Risk, Expected Shortfall

JEL Classification: C22, G15

Suggested Citation

Antola, Matti and Vuorenmaa, Tommi A., Predicting Intraday Price Distributions at High Frequencies (August 9, 2013). Available at SSRN: or

Matti Antola

Valo Research and Trading ( email )

Mannerheimintie 2
6th Floor
Helsinki, 00100

Tommi A. Vuorenmaa (Contact Author)

Triangle Intelligence ( email )

+358-40-7757766 (Phone)


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