Statistical finance

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See also: econophysics , complexity , statistical physics , and financial markets

Contents 1 Statistical finance 1.1 Stylized Facts 1.2 Research Objectives 1.3 Behavioral finance and statistical finance 2 Bibliography

[edit] Statistical finance

Statistical finance ^[1], sometimes called econophysics ^[2], is an empirical attempt to shift finance from its normative roots to a positivist framework using exemplars from statistical physics with an emphasis on emergent or collective properties of financial markets. The starting point for this approach to understanding financial markets are the empirically observed stylized facts.

[edit] Stylized Facts

1. Stock markets are characterised by bursts of price volatility.
2. Price trends are statistically sustained and predictable.
3. Price changes are less volatile in bull markets and more volatile in bear markets.
4. Price change correlations are stronger with higher volatility, and their auto-correlations die out quickly.
5. Almost all real data have more extreme events than suspected.
6. Volatility correlations decay slow enough to make price changes multifractal.
7. Trading volumes have memory the same way that volatilities do.
8. Past price changes are negatively correlated with future volatilities.

[edit] Research Objectives

Statistical finance is focused on three areas:

1. Empirical studies focused on the discovery of interesting statistical features of financial time-series data aimed at extending and consolidating the known stylized facts.
2. The use of these discoveries to build and implement models that better price derivatives and anticipate stock price movement with an emphasis on non-Gaussian methods and models.
3. The study of collective and emergent behaviour in simulated and real markets to uncover the mechanisms responsible for the observed stylized facts with an emphasis on agent based models (see agent based model).

[edit] Behavioral finance and statistical finance

Behavioural finance attempts to explain price anomalies in terms of the biased behaviour of individuals, mostly concerned with the agents themselves and to a lesser degree aggregation of agent behaviour. Statistical finance is concerned with emergent properties arising from systems with many interacting agents and as such attempts to explain price anomalies in terms of the collective behaviour. Emergent properties are largely independent of the uniqueness of individual agents because they are dependent on the nature of the interactions of the agents rather that the agents themselves. This approach draws strongly on ideas arising from complex systems, phase transitions, criticality, self-organized criticality, non-extensivity (see Tsallis entropy), q-Gaussian models, and agents based models (see agent based model); as these are known to be able to recover some of phenomenology of financial market data, the stylized facts, in particular the long-range memory and scaling due to long-range interactions.

References:

1. ^ J-P Bouchaud, An introduction to Statistical Finance, Physica A 313 (2002) 238-251
2. ^ V. Perou, E. Gopikrishnan, L A Amaral, M. Meyer, H. E. Stanley, Phys. Rev. E 60 6519 (1999)

[edit] Bibliography

See Econophysics bibliography and text books

• J-P Bouchaud, M Potters, Theory of Financial Risk and Derivative Pricing, Cambridge University Press (Cambridge, 2004)]

• Rosario N. Mantegna, H. Eugene Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance, Cambridge University Press (Cambridge, 1999)]