Exponentially damped Lévy flights, multiscaling, and exchange rates

✍ Scribed by Raul Matsushita; Iram Gleria; Annibal Figueiredo; Pushpa Rathie; Sergio Da Silva

• Publisher: Elsevier Science
• Year: 2004
• Tongue: English
• Weight: 515 KB
• Volume: 333
• Category: Article
• ISSN: 0378-4371
• DOI: 10.1016/j.physa.2003.10.040

✦ Synopsis

We employ our previously suggested exponentially damped LÃ evy ight (Physica A 326 (2003) 544) to study the multiscaling properties of 30 daily exchange rates against the US dollar together with a ÿctitious euro-dollar rate (Physica A 286 (2000) 353). Though multiscaling is not theoretically seen in either stable LÃ evy processes or abruptly truncated LÃ evy ights, it is even characteristic of smoothly truncated LÃ evy ights (Phys. Lett. A 266 (2000) 282; Eur. Phys. J. B 4 (1998) 143). We have already deÿned a class of "quasi-stable" processes in connection with the ÿnding that single scaling is pervasive among the dollar price of foreign currencies (Physica A 323 (2003) 601). Here we show that the same goes as far as multiscaling is concerned. Our novel ÿndings incidentally reinforce the case for real-world relevance of the LÃ evy ights for modeling ÿnancial prices.