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From Brownian motion to operational risk: Statistical physics and financial markets

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  • Voit, Johannes

Abstract

High-frequency returns of the DAX German blue chip stock index are used to test geometric Brownian motion, the standard model for financial time series. Even on a 15-s time scale, the linear correlations of DAX returns have a zero-time delta function which carries 90% of the weight, while the remaining 10% are positively correlated with a decay time of 53s and negatively correlated on a 9.4-min scale. The probability density of the returns possesses fat tails with power laws whose exponents continuously increase with time scales. It is suggested that hydrodynamic turbulence may provide a phenomenological framework for the description of these data, and at the same time, open a way to use them for risk-management purposes, e.g. option pricing and hedging. Option pricing also is the cornerstone of credit valuation, an area of much practical importance not considered explicitly in most other physics-inspired papers on finance. Finally, operational risk is introduced as a new risk category currently emphasized by regulators, which will become important in many banks in the near future.

Suggested Citation

  • Voit, Johannes, 2003. "From Brownian motion to operational risk: Statistical physics and financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(1), pages 286-299.
    • Handle: RePEc:eee:phsmap:v:321:y:2003:i:1:p:286-299
    DOI: 10.1016/S0378-4371(02)01783-1
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    Cited by:

    1. AlShelahi, Abdullah & Saigal, Romesh, 2018. "Insights into the macroscopic behavior of equity markets: Theory and application," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 505(C), pages 778-793.
    2. Javier Morales & V'ictor Tercero & Fernando Camacho & Eduardo Cordero & Luis L'opez & F-Javier Almaguer, 2014. "Trend and Fractality Assessment of Mexico's Stock Exchange," Papers 1411.3399, arXiv.org.
    3. Münnix, Michael C. & Schäfer, Rudi & Guhr, Thomas, 2010. "Compensating asynchrony effects in the calculation of financial correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 767-779.
    4. Takaishi, Tetsuya, 2018. "Statistical properties and multifractality of Bitcoin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 506(C), pages 507-519.
    5. Morales, Javier & Tercero, Víctor & Camacho-Vallejo, José-Fernando & Cordero, Alvaro E. & López Nerio, Luis E. & Almaguer, F-Javier, 2016. "Trend and fractality assessment of Mexico’s stock exchange," Applied Mathematics and Computation, Elsevier, vol. 285(C), pages 103-113.

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