Abstract
ABSTRACT This study aims to evaluate how the after-market and pre-opening periods affect the estimation of conditional volatility one day ahead. Volatility features quite a lot in Finance studies because it is a fundamental parameter in derivatives pricing, the efficient allocation of portfolios, and risk management. The results are relevant for investment agents to be able to refine volatility forecasting models and achieve better results in derivatives pricing, risk management, and portfolio optimization. We used the asymmetric power autoregressive conditional heteroscedasticity (APARCH) model, incorporating the after-market, pre-opening, and total overnight periods to assess whether they contain important information for modeling volatility. We analyzed the 20 stocks of Brazilian companies listed on the São Paulo Stock, Commodities, and Futures Exchange (BM&FBovespa) and also belonging to the BR Titans 20 with ADRs listed on the New York Stock Exchange and the Nasdaq. The results were evaluated in-sample using the corrected Akaike information criterion (AICc) and the statistical significance of the coefficients, and out-of-sample using root mean squared error (RMSE), mean absolut percentage error (MAPE), the R² of the Mincer-Zarnowitz regression, and the Diebold Mariano test. The analysis does not enable it to be claimed which is the best model, because there is no unanimity among all the stocks; however, non-regular trading hours were shown to incorporate important information for most of the stocks. Furthermore, the models that incorporated the pre-opening period generally obtained superior results to the models that incorporated the after-market period, demonstrating that this period contains important information for forecasting conditional volatility.
Highlights
Breno Valente Fontes Araújo, Marcos Antônio de Camargos & Frank Magalhães de PinhoVarious studies in Brazil and abroad have used daily data to forecast conditional volatility one day ahead
Most of the studies that seek to model the conditional volatility of stocks or indices ignore the variation that occurs between the opening period of one day and the close of the previous day, known as the overnight period
Evaluating the models in-sample, Table 6 indicates the models that presented the best AICc information criterion for each one of the categories, whether these were without the exogenous variable, incorporating the after-market (AM) period, incorporating the pre-opening (OP) period, or incorporating the total overnight (OV) period
Summary
Breno Valente Fontes Araújo, Marcos Antônio de Camargos & Frank Magalhães de Pinho. Various studies in Brazil and abroad have used daily data to forecast conditional volatility one day ahead. The study aims to contribute to the literature in three ways: (i) by presenting an analysis of the overnight period, which has still scarcely been studied in Brazil; (ii) by using sub periods of the non-regular trading hours as explanatory variables for modeling conditional volatility; (iii) by carrying out an out-of-sample analysis, using realized volatility as a parameter, calculated based on intraday data. Past returns do not influence present return, but volatility is correlated with past returns or with “innovations” (residuals) around the mean equation (Tsay, 2010) In his seminal paper, Engle (1982) proposed the ARCH model, in which conditional variance can be modeled using a quadratic function. We chose the APARCH model due to the fact that this study does not aim to evaluate the different models, but rather the impact of the exogenous variables
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