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Modelling of stock price changes: A real analysis approach

Author

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  • Rimas Norvaisa

    () (Institute of Mathematics and Informatics, Akademijos 4, LT-2600 Vilnius, Lithuania Manuscript)

Abstract

In this paper a real analysis approach to stock price modelling is considered. A stock price and its return are defined in a duality to each other provided there exist suitable limits along a sequence of nested partitions of a time interval, mimicking sum and product integrals. It extends the class of stochastic processes susceptible to theoretical analysis. Also, it is shown that extended classical calculus is applicable to market analysis whenever the local 2-variation of sample functions of the return is zero, or is determined by jumps if the process is discontinuous. In particular, an extended Riemann-Stieltjes integral is used in that case to prove several properties of trading strategies.

Suggested Citation

  • Rimas Norvaisa, 2000. "Modelling of stock price changes: A real analysis approach," Finance and Stochastics, Springer, vol. 4(3), pages 343-369.
  • Handle: RePEc:spr:finsto:v:4:y:2000:i:3:p:343-369
    Note: received: October 1997; final version received: June 1999
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    Citations

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    Cited by:

    1. Zhang, H.Y. & Bai, L.H. & Zhou, A.M., 2009. "Insurance control for classical risk model with fractional Brownian motion perturbation," Statistics & Probability Letters, Elsevier, vol. 79(4), pages 473-480, February.
    2. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    3. Alessio Sancetta, 2004. "Copula Based Monte Carlo Integration in Financial Problems," Working Papers wp04-02, Warwick Business School, Finance Group.
    4. Høg, Espen P. & Frederiksen, Per H., 2006. "The Fractional Ornstein-Uhlenbeck Process: Term Structure Theory and Application," Finance Research Group Working Papers F-2006-01, University of Aarhus, Aarhus School of Business, Department of Business Studies.
    5. Xiao, Wei-Lin & Zhang, Wei-Guo & Zhang, Xili & Zhang, Xiaoli, 2012. "Pricing model for equity warrants in a mixed fractional Brownian environment and its algorithm," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(24), pages 6418-6431.
    6. Esben Hoeg & Per Frederiksen, 2006. "The Fractional OU Process: Term Structure Theory and Application," Computing in Economics and Finance 2006 194, Society for Computational Economics.

    More about this item

    Keywords

    continuous-time model; model testing; stock price; return; trading strategy;

    JEL classification:

    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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