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A Markov model of financial returns

Author

Listed:
  • Serva, M.
  • Fulco, U.L.
  • Gléria, I.M.
  • Lyra, M.L.
  • Petroni, F.
  • Viswanathan, G.M.

Abstract

We address the general problem of how to quantify the kinematics of time series with stationary first moments but having non stationary multifractal long-range correlated second moments. We show that a Markov process is sufficient to model important aspects of the multifractality observed in financial time series and propose a kinematic model of price fluctuations. We test the proposed model by analyzing index closing prices of the New York Stock Exchange and the DEM/USD tick-by-tick exchange rates obtained from Reuters EFX. We show that the model captures the characteristic features observed in actual financial time series, including volatility clustering, time scaling and fat tails in the probability density functions, power-law behavior of volatility correlations and, most importantly, the observed nonuniversal multifractal singularity spectrum. Motivated by our finding of strong agreement between the model and the data, we argue that at least two independent stochastic Gaussian variables are required to adequately model price fluctuations.

Suggested Citation

  • Serva, M. & Fulco, U.L. & Gléria, I.M. & Lyra, M.L. & Petroni, F. & Viswanathan, G.M., 2006. "A Markov model of financial returns," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 363(2), pages 393-403.
    • Handle: RePEc:eee:phsmap:v:363:y:2006:i:2:p:393-403
    DOI: 10.1016/j.physa.2005.08.070
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    Cited by:

    1. Silva, L.B.M. & Vermelho, M.V.D. & Lyra, M.L. & Viswanathan, G.M., 2009. "Multifractal detrended fluctuation analysis of analog random multiplicative processes," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2806-2811.
    2. Lu, Changxiang & Ye, Yong & Fang, Yongjun & Fang, Jiaqi, 2023. "An optimal control theory approach for freight structure path evolution post-COVID-19 pandemic," Socio-Economic Planning Sciences, Elsevier, vol. 85(C).
    3. D’Amico, Guglielmo & Petroni, Filippo & Prattico, Flavio, 2013. "First and second order semi-Markov chains for wind speed modeling," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1194-1201.

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