Business Time Sampling Scheme with Applications to Testing Semi-Martingale Hypothesis and Estimating Integrated Volatility

Abstract

Abstract:We propose a new method to implement the Business Time Sampling (BTS) scheme for high-frequency financial data. We compute a time-transformation (TT) function using the intraday integrated volatility estimated by a jump-robust method. The BTS transactions are obtained using the inverse of the TT function. Using our sampled BTS transactions, we test the semi-martingale hypothesis of the stock log-price process and estimate the daily realized volatility. Our method improves the normality approximation of the standardized business-time return distribution. Our Monte Carlo results show that the integrated volatility estimates using our proposed sampling strategy provide smaller root mean-squared error.

Realized Quantiles*

“…4. The business time sampling (BTS) that samples price observations that are equidistant in terms of the intraday price variation, that is, the intensity measure λ(t) is estimated by the jump-robust realized tripower variation estimator of Barndorff-Nielsen, Shephard, and Winkel (2006) on the interval [t − 5min, t + 5min], as in Dong and Tse (2017).…”

“…While TickTS exploits this pattern at the daily basis, TTS, introduced by Wu (2012), aims at capturing its similarity across trading days. The BTS scheme is introduced by Oomen (2005Oomen ( , 2006 and applied by Dong and Tse (2017) with an underlying intensity measure driven by the intraday price variation, which is similar to the intraday trading pattern, but exhibits some differences for stocks as illustrated in Figure 1. Figure 1 provides an example indicating the typical form of the estimated (and smoothed) intensity λ(t) for our sampling schemes for the EURUSD exchange rate and for the IBM stock.…”

“…In the second case, which we adopt in this article, the intrinsic time is defined as a function of a latent intensity measure of the market's activity (Carr and Wu 2004). Empirically, the availability of HF data in the last two decades has opened great possibilities in estimating the intrinsic time directly from the intraday information, through specific choices of intensity measures, such as the trading volume (Mandelbrot and Taylor 1967;Clark 1973;Mandelbrot, Fisher, and Calvet 1997), the intraday volatility pattern (Zhou 1996;Dacorogna et al 2001;Oomen 2005Oomen , 2006; Peters and de Vilder 2006;Andersen, Bollerslev and Diebold 2007;Boudt, Croux, and Laurent 2011;Dong and Tse 2017), the intraday trading pattern (Dacorogna et al 1993;Ghysels, Gouriéroux, and Jasiak 1997;Ané and Geman 2000;Griffin and Oomen 2008;Wu 2012), or in the context of duration models (Engle and Russell 1998;Gerhard and Hautsch 2002). The applications of this approach have stretched from capturing the fat-tailedness of financial returns (Clark 1973;Mandelbrot, Fisher, and Calvet 1997;Marinelli et al 2000) to estimating their spot volatility (Dahlhaus and Tunyavetchakit 2016), RV (Oomen 2005(Oomen , 2006 and stochastic volatility (Tauchen and Pitts 1983;Ghysels, Gouriéroux, andJasiak 1997, 2004) as well as to measuring intraday leverage effects Andersen et al 2010) or for option pricing (Gouriéroux and Jasiak 2001).…”

Uma análise sobre a intensidade da racionalidade do mercado de capitais no intraday

“…A Metodologia de Estudo de Eventos tem a sua origem com os estudos de Dolley (1933) que analisou, no período de 1921 a 1931, os efeitos nos preços das ações em dias próximos à divulgação de 95 desdobramentos de ações (MACKINLAY, 1997). O tema teve destaque com os estudos de Ball et al (1968) ao observarem que os erros ocorridos em informações contábeis entre as previsões e o realizado tinham impacto positivo no índice das ações quando divulgados próximo da data do anúncio do relatório anual.…”

“…Com o avanço tecnológico, a metodologia ampliou seus horizontes e pesquisas têm sido feitas com periodicidade intradiário, que é conhecida na análise de dados de alta frequência. Segundo Dong et al (2017), as atividades de negociação, geralmente, são em maior quantidade no início e no fechamento do dia de negociação e baixas no horário do almoço. Em seus estudos sobre o comportamento das ações do JP Morgan, entre janeiro de 2010de a abril de 2013de , Dong et al (2017 verificou que a volatilidade no início do pregão era aproximadamente duas a três vezes maiores que a próxima do final do pregão, em contraste, o número de transações no final do pregão era duas a três vezes maiores do que no período da manhã.…”