IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/102434.html
   My bibliography  Save this paper

Volatility Depend on Market Trades and Macro Theory

Author

Listed:
  • Olkhov, Victor

Abstract

This paper presents probability distributions for price and returns random processes for averaging time interval Δ. These probabilities determine properties of price and returns volatility. We define statistical moments for price and returns random processes as functions of the costs and the volumes of market trades aggregated during interval Δ. These sets of statistical moments determine characteristic functionals for price and returns probability distributions. Volatilities are described by first two statistical moments. Second statistical moments are described by functions of second degree of the cost and the volumes of market trades aggregated during interval Δ. We present price and returns volatilities as functions of number of trades and second degree costs and volumes of market trades aggregated during interval Δ. These expressions support numerous results on correlations between returns volatility, number of trades and the volume of market transactions. Forecasting the price and returns volatilities depend on modeling the second degree of the costs and the volumes of market trades aggregated during interval Δ. Second degree market trades impact second degree of macro variables and expectations. Description of the second degree market trades, macro variables and expectations doubles the complexity of the current macroeconomic and financial theory.

Suggested Citation

  • Olkhov, Victor, 2020. "Volatility Depend on Market Trades and Macro Theory," MPRA Paper 102434, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:102434
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/102434/1/MPRA_paper_102434.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/103358/1/MPRA_paper_102434.pdf
    File Function: revised version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/103358/8/MPRA_paper_103358.pdf
    File Function: revised version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/121221/1/MPRA_paper_121221.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Brock, William A & LeBaron, Blake D, 1996. "A Dynamic Structural Model for Stock Return Volatility and Trading Volume," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 94-110, February.
    2. Anthony Miloudi & Mondher Bouattour & Ramzi Benkraiem, 2016. "Relationships between Trading Volume, Stock Returns and Volatility: Evidence from the French Stock Market," Bankers, Markets & Investors, ESKA Publishing, issue 144, pages 44-58, September.
    3. David D. Friedman, 1990. "Price Theory: An Intermediate Text," Online economics textbooks, SUNY-Oswego, Department of Economics, number prin13.
    4. Daly, Kevin, 2008. "Financial volatility: Issues and measuring techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(11), pages 2377-2393.
    5. Torben G. Andersen & Tim Bollerslev & Peter F. Christoffersen & Francis X. Diebold, 2005. "Volatility Forecasting," PIER Working Paper Archive 05-011, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania.
    6. N. Gregory Mankiw & David Romer & Matthew D. Shapiro, 1991. "Stock Market Forecastability and Volatility: A Statistical Appraisal," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(3), pages 455-477.
    7. Borovička, Jaroslav & Hansen, Lars Peter, 2014. "Examining macroeconomic models through the lens of asset pricing," Journal of Econometrics, Elsevier, vol. 183(1), pages 67-90.
    8. E. Glen Weyl, 2019. "Price Theory," Journal of Economic Literature, American Economic Association, vol. 57(2), pages 329-384, June.
    9. Alexander Buryak & Ivan Guo, 2014. "Effective And Simple Vwap Options Pricing Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 17(06), pages 1-13.
    10. John Y. Campbell & Sanford J. Grossman & Jiang Wang, 1993. "Trading Volume and Serial Correlation in Stock Returns," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 108(4), pages 905-939.
    11. Ben S. Bernanke & Mark Gertler, 1999. "Monetary policy and asset price volatility," Proceedings - Economic Policy Symposium - Jackson Hole, Federal Reserve Bank of Kansas City, pages 77-128.
    12. W. Erwin Diewert, 1995. "Price and Volume Measures in the System of National Accounts," NBER Working Papers 5103, National Bureau of Economic Research, Inc.
    13. Charlotte Christiansen & Maik Schmeling & Andreas Schrimpf, 2012. "A comprehensive look at financial volatility prediction by economic variables," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 956-977, September.
    14. Gopikrishnan, P. & Plerou, V. & Gabaix, X. & Amaral, L.A.N. & Stanley, H.E., 2001. "Price fluctuations and market activity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 299(1), pages 137-143.
    15. R. F. Engle & A. J. Patton, 2001. "What good is a volatility model?," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 237-245.
    16. Victor Olkhov, 2018. "How Macro Transactions Describe the Evolution and Fluctuation of Financial Variables," IJFS, MDPI, vol. 6(2), pages 1-19, March.
    17. Doron Avramov & Tarun Chordia & Amit Goyal, 2006. "The Impact of Trades on Daily Volatility," The Review of Financial Studies, Society for Financial Studies, vol. 19(4), pages 1241-1277.
    18. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Ebens, Heiko, 2001. "The distribution of realized stock return volatility," Journal of Financial Economics, Elsevier, vol. 61(1), pages 43-76, July.
    19. Olivier Gu'eant & Guillaume Royer, 2013. "VWAP execution and guaranteed VWAP," Papers 1306.2832, arXiv.org, revised May 2014.
    20. Tetsuya Takaishi & Ting Ting Chen, 2017. "The relationship between trading volumes, number of transactions, and stock volatility in GARCH models," Papers 1712.06263, arXiv.org.
    21. George J. Stigler & James K. Kindahl, 1970. "The Behavior of Industrial Prices," NBER Books, National Bureau of Economic Research, Inc, number stig70-1.
    22. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2002. "Parametric and Nonparametric Volatility Measurement," NBER Technical Working Papers 0279, National Bureau of Economic Research, Inc.
    23. V. Plerou & P. Gopikrishnan & X. Gabaix & L. A. N. Amaral & H. E. Stanley, 2001. "Price fluctuations, market activity and trading volume," Quantitative Finance, Taylor & Francis Journals, vol. 1(2), pages 262-269.
    24. Richard B. Heflebower, 1955. "Full Costs, Cost Changes, and Prices," NBER Chapters, in: Business Concentration and Price Policy, pages 361-396, National Bureau of Economic Research, Inc.
    25. Wen-Ling Lin & Takatoshi Ito, 1994. "Price Volatility and Volume Spillovers between the Tokyo and New York Stock Markets," NBER Chapters, in: The Internationalization of Equity Markets, pages 309-343, National Bureau of Economic Research, Inc.
    26. Tauchen, George E & Pitts, Mark, 1983. "The Price Variability-Volume Relationship on Speculative Markets," Econometrica, Econometric Society, vol. 51(2), pages 485-505, March.
    27. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    28. R. L. Hall & C. J. Hitch, 1939. "Price Theory And Business Behaviour," Oxford Economic Papers, Oxford University Press, vol. 0(1), pages 12-45.
    29. George J. Stigler & James K. Kindahl, 1970. "The Dispersion of Price Movements," NBER Chapters, in: The Behavior of Industrial Prices, pages 88-94, National Bureau of Economic Research, Inc.
    30. Enzo Busseti & Stephen Boyd, 2015. "Volume Weighted Average Price Optimal Execution," Papers 1509.08503, arXiv.org.
    31. Emi Nakamura & Jón Steinsson, 2008. "Five Facts about Prices: A Reevaluation of Menu Cost Models," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 123(4), pages 1415-1464.
    32. Merton, Robert C, 1973. "An Intertemporal Capital Asset Pricing Model," Econometrica, Econometric Society, vol. 41(5), pages 867-887, September.
    33. Alexander Buryak & Ivan Guo, 2014. "Effective and simple VWAP option pricing model," Papers 1407.7315, arXiv.org.
    34. Ser-Huang Poon & Clive W.J. Granger, 2003. "Forecasting Volatility in Financial Markets: A Review," Journal of Economic Literature, American Economic Association, vol. 41(2), pages 478-539, June.
    35. Victor Olkhov, 2019. "Financial Variables, Market Transactions, and Expectations as Functions of Risk," IJFS, MDPI, vol. 7(4), pages 1-27, November.
    36. Nicholas C. Barberis, 2018. "Psychology-based Models of Asset Prices and Trading Volume," NBER Working Papers 24723, National Bureau of Economic Research, Inc.
    37. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
    38. Chaiyuth Padungsaksawasdi & Robert T. Daigler, 2018. "Volume weighted volatility: empirical evidence for a new realised volatility measure," International Journal of Banking, Accounting and Finance, Inderscience Enterprises Ltd, vol. 9(1), pages 61-87.
    39. Raymond W. Goldsmith & Robert E. Lipsey, 1963. "Asset Prices and the General Price Level," NBER Chapters, in: Studies in the National Balance Sheet of the United States, Volume 1, pages 166-189, National Bureau of Economic Research, Inc.
    40. Olkhov, Victor, 2017. "Quantitative wave model of macro-finance," International Review of Financial Analysis, Elsevier, vol. 50(C), pages 143-150.
    41. George J. Stigler, Chairman, Universities-National Bureau Committee for Economic Research, 1955. "Business Concentration and Price Policy," NBER Books, National Bureau of Economic Research, Inc, number univ55-1.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Victor Olkhov, 2021. "Three Remarks On Asset Pricing," Papers 2105.13903, arXiv.org, revised Jan 2024.
    2. Olkhov, Victor, 2022. "The Market-Based Asset Price Probability," MPRA Paper 113096, University Library of Munich, Germany.
    3. Olkhov, Victor, 2020. "Price, Volatility and the Second-Order Economic Theory," MPRA Paper 102767, University Library of Munich, Germany.
    4. Olkhov, Victor, 2021. "To VaR, or Not to VaR, That is the Question," MPRA Paper 105458, University Library of Munich, Germany.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Victor Olkhov, 2020. "Price, Volatility and the Second-Order Economic Theory," Papers 2009.14278, arXiv.org, revised Apr 2021.
    2. Victor Olkhov, 2021. "Three Remarks On Asset Pricing," Papers 2105.13903, arXiv.org, revised Jan 2024.
    3. Olkhov, Victor, 2022. "The Market-Based Asset Price Probability," MPRA Paper 113096, University Library of Munich, Germany.
    4. Olkhov, Victor, 2021. "To VaR, or Not to VaR, That is the Question," MPRA Paper 105458, University Library of Munich, Germany.
    5. Olkhov, Victor, 2022. "Why Economic Theories and Policies Fail? Unnoticed Variables and Overlooked Economics," MPRA Paper 114187, University Library of Munich, Germany.
    6. Olkhov, Victor, 2022. "Price and Payoff Autocorrelations in the Consumption-Based Asset Pricing Model," MPRA Paper 112255, University Library of Munich, Germany.
    7. Olkhov, Victor, 2020. "Classical Option Pricing and Some Steps Further," MPRA Paper 105431, University Library of Munich, Germany, revised 28 Dec 2020.
    8. Ralf Remer & Reinhard Mahnke, 2004. "Application of the heston and hull-white models to german dax data," Quantitative Finance, Taylor & Francis Journals, vol. 4(6), pages 685-693.
    9. Olkhov, Victor, 2018. "Expectations, Price Fluctuations and Lorenz Attractor," MPRA Paper 89105, University Library of Munich, Germany.
    10. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    11. Olkhov, Victor, 2023. "Economic Theory as Successive Approximations of Statistical Moments," MPRA Paper 118722, University Library of Munich, Germany.
    12. Bartosz Gębka, 2012. "The Dynamic Relation Between Returns, Trading Volume, And Volatility: Lessons From Spillovers Between Asia And The United States," Bulletin of Economic Research, Wiley Blackwell, vol. 64(1), pages 65-90, January.
    13. Robert Ślepaczuk & Grzegorz Zakrzewski, 2009. "High-Frequency and Model-Free Volatility Estimators," Working Papers 2009-13, Faculty of Economic Sciences, University of Warsaw.
    14. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    15. Peter Christoffersen & Francis X. Diebold, 2002. "Financial Asset Returns, Market Timing, and Volatility Dynamics," CIRANO Working Papers 2002s-02, CIRANO.
    16. Peter F. Christoffersen & Francis X. Diebold, 2006. "Financial Asset Returns, Direction-of-Change Forecasting, and Volatility Dynamics," Management Science, INFORMS, vol. 52(8), pages 1273-1287, August.
    17. Amit K. Sinha, 2021. "The reliability of geometric Brownian motion forecasts of S&P500 index values," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 40(8), pages 1444-1462, December.
    18. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    19. Vipul Kumar Singh, 2013. "Effectiveness of volatility models in option pricing: evidence from recent financial upheavals," Journal of Advances in Management Research, Emerald Group Publishing Limited, vol. 10(3), pages 352-375, October.
    20. Haugom, Erik & Ray, Rina, 2017. "Heterogeneous traders, liquidity, and volatility in crude oil futures market," Journal of Commodity Markets, Elsevier, vol. 5(C), pages 36-49.

    More about this item

    Keywords

    price and returns volatility; price-volume relations; macro theory;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • E00 - Macroeconomics and Monetary Economics - - General - - - General
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G00 - Financial Economics - - General - - - General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
    • G17 - Financial Economics - - General Financial Markets - - - Financial Forecasting and Simulation

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:102434. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.