Impacto dos choques na componente discreta da volatilidade: uma abordagem via ondaletas

Abstract

The presence of jumps has a strong impact on predicting the volatility of financial assets. These jumps can be understood as local structural changes in the series, due to a natural movement of the negotiations, or even as shocks often associated with a behavioral issue of investors, usually caused by macroeconomic news announcements. Therefore, it is imperative to try to understand them well, as it is a challenge to try to predict them. The wavelet approach can be a strong ally in situations like this, since it detects jump locations efficiently, in addition to allowing an economic interpretation by relating the time scales obtained in the decomposition with the investment horizons of the daily life of stock exchange operators. The present work used the universal limit of Donoho and Johnstone to detect jumps in the series obtained with the MODWT wavelet transform of the price series. The jumps detected were then measured and used in the estimation of the Jump Variation (the discrete component of the Quadratic Variation, a natural measure of the variability of the price process). Constructed in this way, it is possible to observe the contribution of the jumps detected in each of the wavelet decomposition time scales to the composition of the Jump Variation, leading to a better understanding of the relevance of each level/horizon for this discontinuous component of the variability of the process. Furthermore, the series of returns can be refined by eliminating the jumps located at the different levels, so that the HAR family models adjusted to these new series reflect the behavior of the Integrated Variance of the process, free from the effects of the jumps. For the study of jumps and a better understanding of their behavior, an application in real data was carried out from the log-price series of Petrobras preferred shares (PETR4), at a frequency of 1 minute, in a period with a strong fall evidenced by an intervention in the presidency of the state-owned company. The methodology used showed that, particularly for this price drop mentioned, the variability due to shocks is impacted in a way that its estimate more than triples when also considering the lower frequency levels, corresponding to investment horizons ranging from minutes to 1 to 2 hours of trading, which also highlights the length of time the news effect takes to dilute in the stock market. The application of the HAR family models showed the presence of a long memory of the realized volatility: both in the traditional HAR-RV model, after eliminating the jumps, and in the HAR-J and HAR-CJ, through their discrete components. Considering the jump robust models showed that eliminating jumps from the wavelet decomposition, in addition to the interpretability that this approach favors, brings more freedom to apply other volatility prediction models that are not restricted to jump robustness.