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# Scaling of the distribution of fluctuations of financial market indices

## Author

Listed:
• Parameswaran Gopikrishnan

(Center for Polymer Studies, Boston University, Boston, MA)

• Vasiliki Plerou

(Center for Polymer Studies, Boston University, Boston, MA)

• Luis A. Nunes Amaral

(Center for Polymer Studies, Boston University, Boston, MA)

• Martin Meyer

(Center for Polymer Studies, Boston University, Boston, MA)

• H. Eugene Stanley

(Center for Polymer Studies, Boston University, Boston, MA)

## Abstract

We study the distribution of fluctuations over a time scale $\Delta t$ (i.e., the returns) of the S&P 500 index by analyzing three distinct databases. Database (i) contains approximately 1 million records sampled at 1 min intervals for the 13-year period 1984-1996, database (ii) contains 8686 daily records for the 35-year period 1962-1996, and database (iii) contains 852 monthly records for the 71-year period 1926-1996. We compute the probability distributions of returns over a time scale $\Delta t$, where $\Delta t$ varies approximately over a factor of 10^4 - from 1 min up to more than 1 month. We find that the distributions for $\Delta t \leq$ 4 days (1560 mins) are consistent with a power-law asymptotic behavior, characterized by an exponent $\alpha \approx 3$, well outside the stable L\'evy regime \$0

## Suggested Citation

• Parameswaran Gopikrishnan & Vasiliki Plerou & Luis A. Nunes Amaral & Martin Meyer & H. Eugene Stanley, 1999. "Scaling of the distribution of fluctuations of financial market indices," Papers cond-mat/9905305, arXiv.org.
• Handle: RePEc:arx:papers:cond-mat/9905305
as

File URL: http://arxiv.org/pdf/cond-mat/9905305

## References listed on IDEAS

as
1. Kirill Ilinski & Alexander Stepanenko, 1999. "Derivative pricing with virtual arbitrage," Papers cond-mat/9902046, arXiv.org.
2. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
4. Hull, John C & White, Alan D, 1987. " The Pricing of Options on Assets with Stochastic Volatilities," Journal of Finance, American Finance Association, vol. 42(2), pages 281-300, June.
Full references (including those not matched with items on IDEAS)

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