Modeling record-breaking stock prices

TL;DR

This paper analyzes the statistics of record-breaking events in stock prices and returns, comparing empirical data with theoretical models like random walks, AR(1), and GARCH(1,1), revealing deviations and improved predictions.

Contribution

It introduces a detailed comparison of stock record statistics with simple and complex models, highlighting deviations and proposing better predictive models such as AR(1) and GARCH(1,1).

Findings

Number of stock records is lower than in simple models.

AR(1) model improves prediction of record statistics.

GARCH(1,1) combined with AR(1) best fits observed data.

Abstract

We study the statistics of record-breaking events in daily stock prices of 366 stocks from the Standard and Poors 500 stock index. Both the record events in the daily stock prices themselves and the records in the daily returns are discussed. In both cases we try to describe the record statistics of the stock data with simple theoretical models. The daily returns are compared to i.i.d. RV's and the stock prices are modeled using a biased random walk, for which the record statistics are known. These models agree partly with the behavior of the stock data, but we also identify several interesting deviations. Most importantly, the number of records in the stocks appears to be systematically decreased in comparison with the random walk model. Considering the autoregressive AR(1) process, we can predict the record statistics of the daily stock prices more accurately. We also compare the stock data with simulations of the record statistics of the more complicated GARCH(1,1) model, which, in combination with the AR(1) model, gives the best agreement with the observational data. To better understand our findings, we discuss the survival and first-passage times of stock prices on certain intervals and analyze the correlations between the individual record events. After recapitulating some recent results for the record statistics of ensembles of N stocks, we also present some new observations for the weekly distributions of record events.