Eryk Lewinson received his master's degree in Quantitative Finance from Erasmus University Rotterdam. In his professional career, he has gained experience in the practical application of data science methods while working in risk management and data science departments of two "big 4" companies, a Dutch neo-broker and most recently the Netherlands' largest online retailer.nOutside of work, he has written over a hundred articles about topics related to data science, which have been viewed more than 3 million times. In his free time, he enjoys playing video games, reading books, and traveling with his girlfriend.
Modeling stock returns' volatility with ARCH models
In this recipe, we approach the problem of modeling the conditional volatility of stock returns with the Autoregressive Conditional Heteroskedasticity (ARCH) model.
To put it simply, the ARCH model expresses the variance of the error term as a function of the past errors. To be a bit more precise, it assumes that the variance of the errors follows an autoregressive (AR) model. The entire logic of the ARCH method can be represented by the following equations:
The first equation represents the return series as a combination of the expected return μ and the unexpected return 𝝐t. 𝝐t has white noise properties—the conditional mean equal to zero and the time-varying conditional variance 𝜎2t. Error terms are serially uncorrelated but do not need to be serially independent, as they can exhibit conditional heteroskedasticity.
is also known as the mean-corrected return, error term, innovations...
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Eryk Lewinson received his master's degree in Quantitative Finance from Erasmus University Rotterdam. In his professional career, he has gained experience in the practical application of data science methods while working in risk management and data science departments of two "big 4" companies, a Dutch neo-broker and most recently the Netherlands' largest online retailer.
Outside of work, he has written over a hundred articles about topics related to data science, which have been viewed more than 3 million times. In his free time, he enjoys playing video games, reading books, and traveling with his girlfriend.
