Olkhov, Victor (2020): Volatility Depend on Market Trades and Macro Theory.
This is the latest version of this item.

PDF
MPRA_paper_102434.pdf Download (236kB)  Preview 


PDF
MPRA_paper_103358.pdf Download (238kB)  Preview 
Abstract
We show that the price and returns volatilities depend on the first and the second degree of the total values and the total volumes of the transactions aggregated during averaging time interval Δ. We derive expressions that describe price volatility via volatilities of the value and the volume and the number of trades during interval Δ. We introduce notions of the value and the volume returns and describe price returns volatility through volatilities of the volume and the value returns and number of trades during Δ. We describe price and returns random processes probability distributions by the complete set of statistical moments determined by corresponding nth degrees products of the values and the volumes of the executed market transactions. Adequate model of volatility requires macroeconomic theory that describes seconddegree value and volume of transactions, the seconddegree macro variables and expectations. This problem doubles the complexity of the current macroeconomic and financial theory.
Item Type:  MPRA Paper 

Original Title:  Volatility Depend on Market Trades and Macro Theory 
English Title:  Volatility Depend on Market Trades and Macro Theory 
Language:  English 
Keywords:  price and returns volatility, pricevolume relations, macro theory 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C10  General E  Macroeconomics and Monetary Economics > E0  General > E00  General E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates > E44  Financial Markets and the Macroeconomy G  Financial Economics > G0  General > G00  General G  Financial Economics > G1  General Financial Markets > G10  General G  Financial Economics > G1  General Financial Markets > G11  Portfolio Choice ; Investment Decisions G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates G  Financial Economics > G1  General Financial Markets > G17  Financial Forecasting and Simulation 
Item ID:  103358 
Depositing User:  Victor Olkhov 
Date Deposited:  09 Oct 2020 11:22 
Last Modified:  05 Aug 2021 15:49 
References:  Andersen, T., Bollerslev, T., Diebold, F.X. and Ebens, H., 2001, The Distribution of Realized Stock Return Volatility, Journal of Financial Economics, 61, 4376. Andersen, T., Bollerslev, T. and F.X. Diebold, 2002, Parametric And Nonparametric Volatility Measurement, NBER, WP 279. Andersen, T.G., Bollerslev, T., Christoffersen, P.F. and F.X. Diebold, 2005, Volatility Forecasting, CFS WP 2005/08, 1116. Avramov, D., Chordia, T., Goyal, A., 2006, The Impact of Trades on Daily Volatility, The Review of Financial Studies, 19, (4), 1241 1277. Berkowitz, S.A., Dennis E. Logue, D.E. and E. A. Noser, Jr., 1988, The Total Cost of Transactions on the NYSE, The Journal Of Finance, 43, (1), 97112. Bernanke, B. and M. Gertler, 1999, Monetary Policy and Asset Price Volatility. FRB of Kansas City, Economic Review, 4Q, 136. Black, F. and M. Scholes, 1973, The Pricing of Options and Corporate Liabilities, The Journal of Political Economy, 81, (3), 637654. Bogousslavsky,V. and P. CollinDufresne, 2019, Liquidity, Volume, and Volatility, Swiss Finance Institute, Research Paper Series 1969, 157. Borovička, J. and L. P. Hansen., 2012, Examining Macroeconomic Models through the Lens of Asset Pricing. FRB Chicago. Brock, W.A. and B.D. LeBaron, 1995, A Dynamic structural model for stock return volatility and trading volume. NBER WP 4988, 146. Buryak,A. and I. Guo, 2014, Effective And Simple VWAP Options Pricing Model, Intern. J. Theor. Applied Finance, 17, (6), 1450036, https://doi.org/10.1142/S0219024914500356 Busseti, E. and S. Boyd, 2015, Volume Weighted Average Price Optimal Execution, 134, arXiv:1509.08503v1 Guéant, O. and G. Royer, 2014, VWAP execution and guaranteed VWAP, SIAM J. Finan. Math., 5(1), 445–471. Campbell, J.Y., Grossman, S.J., Wang, J., 1993, Trading Volume And Serial Correlation In Stock Returns. The Quarterly Journal of Economics, 905939. Christiansen, C., Schmeling, M. and A. Schrimpf, 2012, A Comprehensive Look at Financial Volatility Prediction by Economic Variables. BIS WP 374, 146. Ciner, C. and W. H. Sackley, 2007, Transactions, volume and volatility: evidence from an emerging market, Applied Financial Economics Letters, 3, 161164. CME Group, 2020, www.cmegroup.com/confluence/display/EPICSANDBOX/GovPX+Historical+Data ; www.cmegroup.com/confluence/display/EPICSANDBOX/Standard+and+Poors+500+Futures Cochrane, J.H., 2001, Asset Pricing. Princeton Univ. Press, Princeton, US. Cochrane, J.H. and C.L. Culp, 2003, Equilibrium Asset Pricing and Discount Factors: Overview and Implications for Derivatives Valuation and Risk Management. In Modern Risk Management. A History, Ed. S.Jenkins, 5792. Daly, K., 2008, Financial volatility: Issues and measuring techniques, Physica A 387, 2377–2393. Diewert, E.W., 1995, Price And Volume Measures In The System Of National Accounts. NBER, WP 5103, 165. Engle, R.F. and A.J. Patton, 2001, What good is a volatility model? Quantitative Finance, 1, 237–245. Fama, E.F., 1965, The Behavior of StockMarket Prices. The Journal of Business, 38, (1), 34105. Fetter, F.A., 1912, The Definition of Price. The American Economic Review, 2 (4), 783813. Fox, D.R., et.al. 2019, Concepts and Methods of the U.S. National Income and Product Accounts. BEA, Dep.Commerce, US, Chapters 113, 1 449. Friedman, D.D., 1990, Price Theory: An Intermediate Text. SouthWestern Pub. Co., US. Goldsmith, R.W. and R. E. Lipsey, 1963, Asset Prices and the General Price Level, NBER, 166 – 189, in Studies in the National Balance Sheet of the United States, Ed. Goldsmith, R.W. and R. E. Lipsey. Hall, R.L. and C.J. Hitch, 1939, Price Theory and Business Behaviour, Oxford Economic Papers, 2. Reprinted in T. Wilson and P. W. S. Andrews (eds.), Oxford Studies in the Price Mechanism (Oxford, 1951). Heflebower, R.B., 1955, Full Costs, Cost Changes, and Prices. NBER, 361396, in Business Concentration and Price Policy, Ed. Stigler, G.J., http://www.nber.org/books/univ551 Heston, S.L., 1993, A ClosedForm Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options, The Rev. Financial Studies, 6, (2), 327343. Ito, T. and WL.Lin, 1993, Price Volatility And Volume. Spillovers Between The Tokyo And New York Stock Markets, NBER WP 4592, 133. Klyatskin, V.I., 2005. Stochastic Equations through the Eye of the Physicist, Elsevier B.V. Klyatskin, V.I., 2015. Stochastic Equations: Theory and Applications in Acoustics, Hydrodynamics, Magnetohydrodynamics, and Radiophysics, v.1, 2, Springer, Switzerland Mankiw, N.G., Romer, D. and M.D. Shapiro, 1991, Stock Market Forecastability and Volatility: A Statistical Appraisal, Rev.Economic Studies, 58,455477. Merton, R.C., 1973, An Intertemporal Capital Asset Pricing Model, Econometrica, 41, (5), 867887. Miloudi, A., Bouattour, M., Benkraiem, R., 2016, Relationships between Trading Volume, Stock Returns and Volatility: Evidence from the French Stock Market, Bankers, Markets & Investors, 144, 115. Muth, J.F., 1961, Rational Expectations and the Theory of Price Movements, Econometrica, 29, (3) 315335. Nakamura, E., and J. Steinsson, 2008, Five Facts About Prices: A Reevaluation Of Menu Cost Models. The Quarterly Jour. of Economics, 14151464. Plerou, V., Gopikrishnan, P., Gabaix, X., Amaral, L.A., and H. E. Stanley, 2001, Price fluctuations, market activity and trading volume, Quantitative Finance, 1, 262–269. Padungsaksawasdi, C., and R. T. Daigler, 2018, Volume weighted volatility: empirical evidence for a new realized volatility measure, Int. J. Banking, Accounting and Finance, 9, (1), 6187. Poon, SH., and C.W.J. Granger, 2003, Forecasting Volatility in Financial Markets: A Review, J. of Economic Literature, 41, 478–539. Shiryaev, A.N., 1999. Essentials of Stochastic Finance: Facts, Models, Theory, World Scientific Pub.Co., Singapore Stigler, G.J., and J.K. Kindahl, 1970, The Dispersion of Price Movements, NBER, 88  94 in Ed. Stigler,G.J., and J.K. Kindahl ,The Behavior of Industrial Prices Takaishi, T., and T. T. Chen, 2017, The relationship between trading volumes, number of transactions, and stock volatility in GARCH models, J. Phys., Conf. Ser. 738 012097, 14, doi:10.1088/17426596/738/1/012097. Tauchen, G.E. and M. Pitts, 1983, The Price VariabilityVolume Relationship On Speculative Markets, Econometrica, 51, (2), 485505. Weyl, E.G., 2019, Price Theory, AEA J. of Economic Literature, 57(2), 329–384. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/103358 
Available Versions of this Item

Volatility Depend on Market Trades and Macro Theory. (deposited 15 Aug 2020 14:36)
 Volatility Depend on Market Trades and Macro Theory. (deposited 09 Oct 2020 11:22) [Currently Displayed]