Jump detection in financial asset prices that exhibit U-shape volatility

We describe a Matlab routine that allows us to estimate the jumps in financial asset prices using the Threshold (or Truncation) method of Mancini (2009). The routine is designed for application to five-minute log-returns. The underlying assumption is that asset prices evolve in time following an Ito semimartingale with, possibly stochastic, volatility and jumps. A log-return is likely to contain a jump if its absolute value is larger than a threshold determined by the maximum increment of the Brownian semimartingale part. The latter is particularly sensitive to the magnitude of the volatility coefficient, and from an empirical point of view, volatility levels typically depend on the time of day (TOD), with volatility being highest at the beginning and end of the day, while it is low in the middle. The first routine presented allows for an estimation of the TOD effect, and is an implementation of the method described in Bollerslev and Todorov (2011). Subsequently, the TOD effect for the stock Apple Inc. (AAPL) is visualized. The second routine presented is an implementation of the threshold method for estimating jumps in AAPL prices. The procedure recursively estimates daily volatility and jumps. In each round, the threshold depends on the time of the day and is constructed using the estimate of the daily volatility multiplied by the daytime TOD factor and by the continuity modulus of the Brownian motion paths. Once the jumps are detected, the daily volatility estimate is updated using only the log-returns not containing jumps. Before application to empirical data, the reliability of the procedure was separately tested on simulated asset prices. The results obtained on a record of AAPL stock prices are visualized.