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Scaling Foreign Exchange Volatility

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Abstract

When asset returns are normally distributed the risk of an asset over a long return interval may be estimated by scaling the risk from shorter return intervals. While it is well known that asset returns are not normally distributed a key empirical question concerns the effect that scaling the volatility of dependent processes will have on the pricing of related financial assets. This study provides an insight into this issue by investigating the return properties of the most important currencies traded in spot markets against the U.S. dollar: the Deutsche mark, the Swiss franc, the Japanese yen, and the British pound, during the period from January 1985 to December 1998. The novelty of this paper is that the volatility properties of the series are tested utilizing statistical procedures developed from fractal geometry after adjusting for dependence in the series, with the economic impact determined within an option-pricing framework. The results demonstrate that scaling risk underestimates the actual level of risk for all four series investigated. However while the call and put premiums on Deutsche mark, Swiss franc and yen options are too low, those on the English pound are not. In our discussion of the possible sources of option under-pricing both conditional heteroskedasticity and underpricing bias by the Black-Scholes model have been considered. However, these factors were unable to account for the very high levels of underpricing reported. In conclusion, these results highlight the complex behaviour of financial asset returns and the inability of general pricing models to completely and accurately describe this behaviour.

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File URL: http://www.deakin.edu.au/buslaw/aef/workingpapers/papers/wpa01_01.pdf
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Bibliographic Info

Paper provided by Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance in its series Accounting, Finance, Financial Planning and Insurance Series with number 2001_01.

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Length: 40 pages
Date of creation: 21 Jan 2001
Date of revision:
Handle: RePEc:dkn:acctwp:aef_2001_01

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Keywords: Scaling volatility; long-term dependence; foreign exchange;

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References

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  1. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  2. Cheung, Yin-Wong, 1993. "Long Memory in Foreign-Exchange Rates," Journal of Business & Economic Statistics, American Statistical Association, vol. 11(1), pages 93-101, January.
  3. Schwert, G William, 2002. "Tests for Unit Roots: A Monte Carlo Investigation," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 5-17, January.
  4. Eugene F. Fama, . "Market Efficiency, Long-term Returns, and Behavioral Finance," CRSP working papers 340, Center for Research in Security Prices, Graduate School of Business, University of Chicago.
  5. Batten, Jonathan & Ellis, Craig & Fetherston, Thomas A., 2000. "Are long-term return anomalies illusions?: Evidence from the spot Yen," Japan and the World Economy, Elsevier, vol. 12(4), pages 337-349, December.
  6. Brock, William & Lakonishok, Josef & LeBaron, Blake, 1992. " Simple Technical Trading Rules and the Stochastic Properties of Stock Returns," Journal of Finance, American Finance Association, vol. 47(5), pages 1731-64, December.
  7. Allan Timmermann & Halbert White & Ryan Sullivan, 1998. "Data-Snooping, Technical Trading, Rule Performance and the Bootstrap," FMG Discussion Papers dp303, Financial Markets Group.
  8. van de Gucht, Linda M. & Dekimpe, Marnik G. & Kwok, Chuck C. Y., 1996. "Persistence in foreign exchange rates," Journal of International Money and Finance, Elsevier, vol. 15(2), pages 191-220, April.
  9. Batten, Jonathan & Craig Ellis, 2001. "Scaling Relationships of Gaussian Processes," Accounting, Finance, Financial Planning and Insurance Series 2001_02, Deakin University, Faculty of Business and Law, School of Accounting, Economics and Finance.
  10. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
  11. Lo, Andrew W. (Andrew Wen-Chuan), 1989. "Long-term memory in stock market prices," Working papers 3014-89., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  12. Pagan, Adrian, 1996. "The econometrics of financial markets," Journal of Empirical Finance, Elsevier, vol. 3(1), pages 15-102, May.
  13. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
  14. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
  15. Gucht, L. van de & Dekimpe, M.G. & Kwok, C., 1996. "Persistence in foreign exchange rates," Open Access publications from Tilburg University urn:nbn:nl:ui:12-358837, Tilburg University.
  16. Barkoulas, John T & Labys, Walter C & Onochie, Joseph I, 1999. "Long Memory In Futures Prices," The Financial Review, Eastern Finance Association, vol. 34(1), pages 91-100, February.
  17. Jin-Chuan Duan, 1995. "The Garch Option Pricing Model," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 13-32.
  18. Tucker, Alan L & Pond, Lallon, 1988. "The Probability Distribution of Foreign Exchange Price Changes: Tests of Candidate Processes," The Review of Economics and Statistics, MIT Press, vol. 70(4), pages 638-47, November.
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Cited by:
  1. Jamdee, Sutthisit & Los, Cornelis A., 2007. "Long memory options: LM evidence and simulations," Research in International Business and Finance, Elsevier, vol. 21(2), pages 260-280, June.

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