A semi-Markov model with memory for price changes

Abstract

We study the high-frequency price dynamics of traded stocks by means of a modelof returns using a semi-Markov approach. More precisely we assume that theintraday returns are described by a discrete time homogeneous semi-Markov modelwhich depends also on a memory index. The index is introduced to take intoaccount periods of high and low volatility in the market. First of all we derive theequations governing the process and then theoretical results are compared withempirical findings from real data. In particular we analyzed high-frequency datafrom the Italian stock market from 1 January 2007 until the end of December2010.