Abstract
A theory which describes the share price evolution at financial markets as a continuous-time random walk (Physica A 287 (2000) 468, Physica A 314 (2002) 749, Eur. Phys. J. B 27 (2002) 273, Physica A 376 (2000) 284) has been generalized in order to take into account the dependence of waiting times t on price returns x. A joint probability density function (pdf) φ X , T ( x , t ) which uses the concept of a Lévy stable distribution is worked out. The theory is fitted to high-frequency US $/Japanese Yen exchange rate and low-frequency 19th century Irish stock data. The theory has been fitted both to price return and to waiting time data and the adherence to data, in terms of the χ 2 test statistic, has been improved when compared to the old theory.
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