The Confidence Limits of a Geometric Brownian Motion
This paper investigates whether the assumption of Brownian motion often used to describe commodity price movements is satisfied. Using historical data from 17 commodity futures contracts specific tests of fractional and ordinary Brownian motion are conducted. The analyses are conducted under the null hypothesis of ordinary Brownian motion against the alternative of persistent or ergodic fractional Brownian motion. Tests for fractional Brownian motion are based on a variance ratio test. However, standard errors based on Monte Carlo simulations are quite high, meaning that the acceptance region for the null hypothesis is large. The results indicate that for the most part, the null hypothesis of ordinary Brownian motion cannot be rejected for 14 of 17 series. The three series that did not satisfy the tests were rejected because they violated the stationarity property of the random walk hypothesis.
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- Boyle, Phelim & Broadie, Mark & Glasserman, Paul, 1997. "Monte Carlo methods for security pricing," Journal of Economic Dynamics and Control, Elsevier, vol. 21(8-9), pages 1267-1321, June.
- Marco Corazza & A.G. Malliaris & Carla Nardelli, 1997. "Searching for fractal structure in agricultural futures markets," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 17(4), pages 433-473, 06.
- Billy P. Helms & Fred R. Kaen & Robert E. Rosenman, 1984. "Memory in commodity futures contracts," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 4(4), pages 559-567, December.
- Black, Fischer, 1976. "The pricing of commodity contracts," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 167-179.
- Hyun J. Jin & Darren L. Frechette, 2004. "Fractional Integration in Agricultural Futures Price Volatilities," American Journal of Agricultural Economics, Agricultural and Applied Economics Association, vol. 86(2), pages 432-443.
- B. Mandelbrot, 1972. "Statistical Methodology for Nonperiodic Cycles: From the Covariance To R/S Analysis," NBER Chapters,in: Annals of Economic and Social Measurement, Volume 1, number 3, pages 259-290 National Bureau of Economic Research, Inc.
- Benoit Mandelbrot, 2015.
"The Variation of Certain Speculative Prices,"
World Scientific Book Chapters,in: THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78
World Scientific Publishing Co. Pte. Ltd..
- Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394-394.
- Fama, Eugene F & French, Kenneth R, 1988. "Permanent and Temporary Components of Stock Prices," Journal of Political Economy, University of Chicago Press, vol. 96(2), pages 246-273, April.
- Booth, G. Geoffrey & Kaen, Fred R. & Koveos, Peter E., 1982. "R/S analysis of foreign exchange rates under two international monetary regimes," Journal of Monetary Economics, Elsevier, vol. 10(3), pages 407-415.
- 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.
- Barkoulas, John T. & Baum, Christopher F., 1996. "Long-term dependence in stock returns," Economics Letters, Elsevier, vol. 53(3), pages 253-259, December.
- Christopher F. Baum & John Barkoulas, 1996. "Long Term Dependence in Stock Returns," Boston College Working Papers in Economics 314., Boston College Department of Economics.
- Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "An Intertemporal General Equilibrium Model of Asset Prices," Econometrica, Econometric Society, vol. 53(2), pages 363-384, March.
- Comte, F. & Renault, E., 1996. "Long memory continuous time models," Journal of Econometrics, Elsevier, vol. 73(1), pages 101-149, July.
- L. C. G. Rogers, 1997. "Arbitrage with Fractional Brownian Motion," Mathematical Finance, Wiley Blackwell, vol. 7(1), pages 95-105.
- P. S. Sephton, 2002. "Fractional cointegration: Monte Carlo estimates of critical values, with an application," Applied Financial Economics, Taylor & Francis Journals, vol. 12(5), pages 331-335. Full references (including those not matched with items on IDEAS)
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