Modeling share price evolution as a continuous time random walk (CTRW) with non-independent price changes and waiting times

A theory which describes the share price evolution at financial markets as a continuous time random walk has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function phi(X,T)(x, t), which uses the concept of a Levy stable distribution, is worked out. The evolution equation is formulated and it is shown that the process is non-Markovian. Finally, the theory is fitted to market data. (C) 2004 Elsevier B.V. All rights reserved.