Skip to main content Accessibility help

We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.

Close cookie message
×
Hostname: page-component-cd9895bd7-lnqnp Total loading time: 0 Render date: 2024-12-23T06:55:57.100Z Has data issue: false hasContentIssue false

2 - The Statistics of Price Changes: An Informal Primer

from PART I - HOW AND WHY DO PRICES MOVE?

Published online by Cambridge University Press:  26 February 2018

Jean-Philippe Bouchaud ,
Julius Bonart ,
Jonathan Donier  and
Martin Gould
Jean-Philippe Bouchaud
Affiliation:
Capital Fund Management, Paris
Julius Bonart
Affiliation:
University College London
Jonathan Donier
Affiliation:
Capital Fund Management
Martin Gould
Affiliation:
CFM - Imperial Institute of Quantitative Finance
Get access

Summary

If you are going to use probability to model a financial market, then you had better use the right kind of probability. Real markets are wild.

(Benoît B. Mandelbrot)

During the past 40 years, financial engineering has grown tremendously. Today, both the financial industry and its regulators rely heavily on a wide range of models to address many different phenomena on many different scales. These models serve as tools to inform trading decisions and assess risk in a diverse set of applications, including risk management, risk control, portfolio construction, derivative pricing, hedging, and even market design.

Among these models, the most widely used are those that seek to describe changes in an asset's price. Given their prominence, it is important to consider the extent to which these models really reflect empirically observed price series, because models whose assumptions are at odds with real markets are likely to produce poor output. Also, because so much of the modern financial world relies on such models so heavily, widespread application of unsuitable models can create unstable feedback loops and lead to the emergence of system-wide instabilities. For example, the severe market crash in 1987 is often attributed to the prevalence of models that assumed independent Gaussian price returns, and thereby severely underestimated the probability of large price changes. Bizarrely, financial crises can be induced by the very models designed to prevent them.

Market crashes serve as a wake-up call to reject idealistic simplifications and to move towards a more realistic framework that encompasses the real statistical properties of price changes observable in empirical data. Despite considerable recent effort in this direction, this goal remains elusive, due partly to the fact that many of the statistical properties of real price series are highly non-trivial and sometimes counter-intuitive. These statistical properties are called the stylised facts of financial price series.

The aim of this chapter is to provide an informal introduction to the most important of these stylised facts. In addition to being interesting in their own right, these stylised facts constitute a set of quantitative criteria against which to evaluate models’ outputs. As we discuss throughout the chapter, a model's inability to reproduce one or more stylised facts can be used as an indicator for how it needs to be improved, or even as a reason to rule it out altogether.

Type
Chapter
Information
Trades, Quotes and Prices
Financial Markets Under the Microscope
 , pp. 22 - 40
Publisher: Cambridge University Press
Print publication year: 2018

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Bachelier, L. (1900). Théorie de la spéculation. Gauthier-Villars.Google Scholar
Frisch, U. (1997). Turbulence: The Kolmogorov legacy. Cambridge University Press.Google Scholar
Mantegna, R. N., & Stanley, H. E. (1999). Introduction to econophysics: correlations and complexity in finance. Cambridge University Press.CrossRefGoogle Scholar
Shiller, R. J. (2000). Irrational exuberance. Princeton University Press.Google Scholar
Lyons, R. K. (2001). The microstructure approach to exchange rates.(Vol. 12). MIT Press.Google Scholar
Bouchaud, J. P., & Potters, M. (2003). Theory of financial risk and derivative pricing: From statistical physics to risk management. Cambridge University Press.CrossRefGoogle Scholar
Andersen, T. G., Davis, R. A., Kreiss, J. P., & Mikosch, T. V. (Eds.). (2009). Handbook of financial time series. Springer Science & Business Media.Google Scholar
Slanina, F. (2013). Essentials of econophysics modelling. Oxford University Press.CrossRefGoogle Scholar
Guillaume, D. M., Dacorogna, M. M., Davé, R. R., Muller, U. A., Olsen, R. B., & Pictet, O. V. (1997). From the bird's eye to the microscope: A survey of new stylised facts of the intra-daily foreign exchange markets. Finance and Stochastics, 1(2), 95–129.CrossRefGoogle Scholar
Gopikrishnan, P., Plerou, V., Amaral, L. A. N., Meyer, M., & Stanley, H. E. (1999). Scaling of the distribution of fluctuations of financial market indices. Physical Review E, 60(5), 5305.CrossRefGoogle ScholarPubMed
Plerou, V., Gopikrishnan, P., Amaral, L. A. N., Meyer, M., & Stanley, H. E. (1999). Scaling of the distribution of price fluctuations of individual companies. Physical Review E, 60(6), 6519.CrossRefGoogle ScholarPubMed
Andersen, T. G. T., Diebold, F. X., & Ebens, H. (2001). The distribution of realised stock return volatility. Journal of Financial Economics, 61(1), 43–76.CrossRefGoogle Scholar
Cont, R. (2001). Empirical properties of asset returns: Stylised facts and statistical issues. Quantitative Finance, 1, 223–236.CrossRefGoogle Scholar
Gabaix, X., Gopikrishnan, P., Plerou, V., & Stanley, H. E. (2006). Institutional investors and stock market volatility. The Quarterly Journal of Economics, 121(2), 461–504.CrossRefGoogle Scholar
Zumbach, G., & Finger, C. (2010). A historical perspective on market risks using the DJIA index over one century. Wilmott Journal, 2(4), 193–206.CrossRefGoogle Scholar
Diebold, F. X., & Strasser, G. (2013). On the correlation structure of microstructure noise: A financial economic approach. The Review of Economic Studies, 80(4), 1304–1337.CrossRefGoogle Scholar
Bollerslev, T., Engle, R. F., & Nelson, D. B. (1994). ARCH models. In Engle, R. & McFadden, D. (Eds.), Handbook of econometrics (Vol. 4, pp. 2959–3028).
North-Holland. Muzy, J. F., Delour, J., & Bacry, E. (2000). Modelling fluctuations of financial time series: From cascade process to stochastic volatility model. The European Physical Journal B-Condensed Matter and Complex Systems, 17(3), 537–548.Google Scholar
Bouchaud, J. P. (2001). Power-laws in economics and finance: Some ideas from physics. Quantitative Finance, 1, 105–112.CrossRefGoogle Scholar
Sethna, J. P., Dahmen, K. A., & Myers, C. R. (2001). Crackling noise. Nature, 410(6825), 242–250.CrossRefGoogle ScholarPubMed
Cabrera, J. L., & Milton, J. G. (2002). On-off intermittency in a human balancing task. Physical Review Letters, 89(15), 158702.CrossRefGoogle Scholar
Calvet, L., & Fisher, A. (2002). Multifractality in asset returns: Theory and evidence. Review of Economics and Statistics, 84(3), 381–406.CrossRefGoogle Scholar
Lux, T. (2008). The Markov-switching multifractal model of asset returns: GMM estimation and linear forecasting of volatility. Journal of Business and Economic Statistics, 26, 194–210.CrossRefGoogle Scholar
Clauset, A., Shalizi, C. R., & Newman, M. E. (2009). Power-law distributions in empirical data. SIAM Review, 51(4), 661–703.CrossRefGoogle Scholar
Gabaix, X. (2009). Power laws in economics and finance. Annual Review of Economics, 1(1), 255–294.CrossRefGoogle Scholar
Patzelt, F., & Pawelzik, K. (2011). Criticality of adaptive control dynamics. Physical Review Letters, 107(23), 238103.CrossRefGoogle ScholarPubMed
Gatheral, J., Jaisson, T., & Rosenbaum, M. (2014). Volatility is rough. arXiv preprint arXiv:1410.3394.
Gnedenko, B. V., & Kolmogorov, A. N. (1968). Limit distributions for sums of independent random variables. 2nd Edn., Addison-Wesley.Google Scholar
Embrechts, P., Klüppelberg, C., & Mikosch, T. (1997). Modelling extremal events. Springer-Verlag.CrossRefGoogle Scholar
Malevergne, Y., & Sornette, D. (2006). Extreme financial risks: From dependence to risk management. Springer Science & Business Media.Google Scholar
Shiller, R. J. (1980). Do stock prices move too much to be justified by subsequent changes in dividends? American Economic Review, 71, 421–436.Google Scholar
Cutler, D. M., Poterba, J. M., & Summers, L. H. (1989). What moves stock prices. The Journal of Portfolio Management, 15(3), 4–12.CrossRefGoogle Scholar
Fair, R. C. (2002). Events that shook the market. The Journal of Business, 75(4), 713–731.CrossRefGoogle Scholar
Gillemot, L., Farmer, J. D., & Lillo, F. (2006). There's more to volatility than volume. Quantitative Finance, 6(5), 371–384.CrossRefGoogle Scholar
Joulin, A., Lefevre, A., Grunberg, D., & Bouchaud, J. P. (2008). Stock price jumps: News and volume play a minor role. Wilmott Magazine, September/October, 1–7.
Bouchaud, J. P. (2011). The endogenous dynamics of markets: Price impact, feedback loops and instabilities. In Berd, A. (Ed.), Lessons from the credit crisis. Risk Publications.Google Scholar
Cornell, B. (2013). What moves stock prices: Another look. The Journal of Portfolio Management, 39(3), 32–38.CrossRefGoogle Scholar
Diebold, F. X., & Strasser, G. (2013). On the correlation structure of microstructure noise: A financial economic approach. The Review of Economic Studies, 80(4), 1304–1337.CrossRefGoogle Scholar
Bondt, W. F., & Thaler, R. (1985). Does the stock market overreact. The Journal of Finance, 40(3), 793–805.CrossRefGoogle Scholar
Black, F. (1986). Noise. The Journal of Finance, 41(3), 528–543.CrossRefGoogle Scholar
Summers, L. H. (1986). Does the stock market rationally reflect fundamental values. The Journal of Finance, 41(3), 591–601.CrossRefGoogle Scholar
Shleifer, A., & Summers, L. H. (1990). The noise trader approach to finance. The Journal of Economic Perspectives, 4(2), 19–33.Google Scholar
Lyons, R. (2001). The microstructure approach to foreign exchange rates. MIT Press.Google Scholar
Schwert, G. W. (2003). Anomalies and market efficiency. In Constantinides, G. M., Harris, M., & Stulz, R. (Eds.), Handbook of the economies of finance (Vol. 1, pp. 939–974).Google Scholar
Elsevier Science, B.V., Lo, A. W. (2017). Adaptive markets. Princeton University Press.Google Scholar

Save book to Kindle

To save this book to your Kindle, first ensure [email protected] is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

Available formats
×