May 16, 2011
Continuous-Time Model of Equity Returns
HERE is another interesting study. It tries to find a mathematical model for daily stock prices at the 5-minute level. All should recognize the u-shaped volatility curve exhibited during trading hours. The paper presents the case where the data should dictate the structure of the model and where the model, while not perfect, should capture and explain most of the daily fluctuations.
The authors conclude that with their view of the data structure and accounting for data seasonality, prices have a near-Gaussian distribution, which is another way of saying that prices at the 5-minute level are quasi-random.
Faced with such a conclusion, one should (at least at the 5-minute level) adopt, more closely, a gaming strategy with all its implications.