Olkhov, Victor (2020): Price, Volatility and the SecondOrder Economic Theory.
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Abstract
We introduce the price probability measure η(p;t) that defines the mean price p(1;t), mean square price p(2;t), price volatility σp2(t) and all price nth statistical moments p(n;t) as ratio of sums of nth degree values C(n;t) and volumes U(n;t) of market trades aggregated during certain time interval Δ. The definition of the mean price p(1;t) coincides with definition of the volume weighted average price (VWAP) introduced at least 30 years ago. We show that price volatility σp2(t) forecasting requires modeling evolution of the sums of seconddegree values C(2;t) and volumes U(2;t). We call this model as secondorder economic theory. We use numerical continuous risk ratings as ground for risk assessment of economic agents and distribute agents by risk ratings as coordinates. We introduce continuous economic media approximation of squares of values and volumes of agents trades and their flows aggregated during time interval Δ. We take into account expectations that govern agents trades and introduce aggregated expectations alike to aggregated trades. We derive equations for continuous economic media approximation on the seconddegree trades. In the linear approximation we derive mean square price p(2;t) and volatility σp2(t) disturbances as functions of the first and seconddegree trades disturbances. Description of each next nth price statistical moment p(n;t) with respect to the unit price measure η(p;t) depends on sums of nth degree values C(n;t) and volumes U(n;t) of market trades and hence requires development of the corresponding nth order economic theory.
Item Type:  MPRA Paper 

Original Title:  Price, Volatility and the SecondOrder Economic Theory 
English Title:  Price, Volatility and the SecondOrder Economic Theory 
Language:  English 
Keywords:  price probability; volatility; economic theory; market transactions; expectations 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General D  Microeconomics > D4  Market Structure, Pricing, and Design E  Macroeconomics and Monetary Economics > E4  Money and Interest Rates G  Financial Economics > G1  General Financial Markets G  Financial Economics > G2  Financial Institutions and Services 
Item ID:  107316 
Depositing User:  Victor Olkhov 
Date Deposited:  26 Apr 2021 13:11 
Last Modified:  26 Apr 2021 13:11 
References:  Andersen, T., Bollerslev, T., Diebold, F. & Ebens, H. (2001). The Distribution of Realized Stock Return Volatility. Journal of Financial Economics, 61, 4376 Andersen, T.G., Bollerslev, T., Christoffersen, P.F. & Diebold, F.X. (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 Beaver, W. H., Shakespeare, C. & Soliman, M.T. (2006). Differential properties in the ratings of certified versus noncertified bondrating agencies. Journal of Accounting and Economics, 42, 303–334 Belkin, B., Suchower, S. & Forest, L.R. (1998). A oneparameter representation of credit risk and transition matrices. JP Morgan, CreditMetrics® Monitor, 3d Q, 4656 Berkowitz, S.A., Dennis E. Logue, D.E. & Noser, E.A. Jr. (1988). The Total Cost of Transactions on the NYSE, The Journal of Finance, 43, (1), 97112 Bernanke, B. & Gertler, M. (1999). Monetary Policy and Asset Price Volatility. FRB of Kansas City, Economic Review, 4Q, 136 Blume, L.E. & Easley, D. (1984). Rational Expectations Equilibrium: An Alternative Approach. Journal Of Economic Theory, 34, 116129 Bogousslavsky,V. & CollinDufresne, P. (2019). Liquidity, Volume, and Volatility, Swiss Finance Institute, Research Paper Series 1969, 157 Brock, W.A. & LeBaron, B.D. (1995). A Dynamic structural model for stock return volatility and trading volume. NBER WP, 4988, 146 Brunnermeier, M.K. & Parker, J.A. (2005). Optimal Expectations. American Economic Review, 95, (4), 10921118 Buryak, A. & Guo, I. (2014). Effective And Simple VWAP Options Pricing Model, Intern. J. Theor. Applied Finance, 17, (6), 1450036, https://doi.org/10.1142/S0219024914500356 Busseti, E. & Boyd, S. (2015). Volume Weighted Average Price Optimal Execution, 134, arXiv:1509.08503v1 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. & Schrimpf, A. (2012). A Comprehensive Look at Financial Volatility Prediction by Economic Variables. BIS WP, 374, 146 Ciner, C. & Sackley, W. H. (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 Daly, K. (2008). Financial volatility: Issues and measuring techniques, Physica A 387, 2377–2393 Dominitz, J. & Manski, C.F. (2005). Measuring And Interpreting Expectations Of Equity Returns. NBER, WP 11313, Cambridge, MA Durand, D. (1941). Volume Title: Risk Elements in Consumer Instalment Financing, Technical Edition, NBER, http://www.nber.org/books/dura411 Engle, R.F. & Patton, A.J. (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 Fitch, (2018). Procedures and Methodologies for Determining Credit Ratings. Fitch Ratings, Inc., Form 25101F1 Greenwood, R. & Shleifer, A. (2014). Expectations of Returns and Expected Returns. The Review of Financial Studies, 27 (3), 714–746 Guéant, O. & Royer, G. (2014). VWAP execution and guaranteed VWAP, SIAM J. Finan. Math., 5(1), 445–471 Hall, R.L. & Hitch, C.J. (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) 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 Ho, A., et.al. (2017). AsiaPacific Structured Finance 2016 Transition and Default Study, FitchRatings Structured Finance, 114 Ito, T. & WL.Lin, (1993). Price Volatility And Volume. Spillovers Between The Tokyo And New York Stock Markets, NBER WP 4592, 133 Janžek, T. & Ziherl, P. (2013). Overview of models and methods for measuring economic agent’s expectations. BIS, IFC Bulletin 36, 172179. https://www.bis.org/ifc/publ/ifcb36.htm 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 Lucas, R.E. (1972). Expectations and the Neutrality of Money. J. Econ. Theory, 4, 103124 Mankiw, N.G., Romer, D. & Shapiro, M.D. (1991). Stock Market Forecastability and Volatility: A Statistical Appraisal, Rev.Economic Studies, 58,455477 Manski, C. (2004). Measuring Expectations. Econometrica, 72, 13291376 Manski, C.F. (2017). Survey Measurement Of Probabilistic Macroeconomic Expectations: Progress and Promise. NBER, WP 23418 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 Moody’s, (2010). Rating Symbols and Definitions. Moody’s Investors Service Moody’s, (2018). Procedures and Methodologies Used to Determine Credit Ratings. Moody’s Investors Service Muth, J.F. (1961). Rational Expectations and the Theory of Price Movements, Econometrica, 29, (3) 315335 Myers, J.H. & Forgy, E.W. (1963). The Development of Numerical Credit Evaluation Systems, Jour. American Statistical Association, 58, 303, 799806 Olkhov, V. (2016a). On Economic space Notion. Intern. Rev. Financial Analysis, 47, 372–81 Olkhov, V. (2016b). Finance, Risk and Economic space. ACRN Oxford Journal of Finance and Risk Perspectives, 5, 209–21 Olkhov, V. (2017a). Quantitative Wave Model of MacroFinance. Intern. Rev. Financial Analysis, 50, 143–50 Olkhov, V. (2017b). Econophysics of Business Cycles: Aggregate Economic Fluctuations, Mean Risks and Mean Square Risks, 131, http://arxiv.org/abs/1709.00282 Olkhov, V. (2018). How Macro Transactions Describe the Evolution and Fluctuation of Financial Variables. Intern. Jour. Financial Studies, 6, 38, 119 Olkhov, V. (2019a). Economic Transactions Govern Business Cycles. ACRN Oxford Journal of Finance and Risk Perspectives, 7, 102–22 Olkhov, V. (2019b). Financial Variables, Market Transactions, and Expectations as Functions of Risk. Int. Jour. Financial Stud., 7, 66, 127 Olkhov, V. (2019c). The Econophysics Of Asset Prices, Returns And Multiple Expectations. The Journal of Network Theory in Finance, 5 (3), 2552 Olkhov, V. (2020). Volatility depend on Market Trades and Macro Theory. MPRA WP 102434 Padungsaksawasdi, C., & Daigler, R. T. (2018). Volume weighted volatility: empirical evidence for a new realized volatility measure, Int. J. Banking, Accounting and Finance, 9, (1), 6187 Pearce, D.K. (1983). Stock Prices and the Economy. FRB Kansas, Economic Review, 722 Poon, SH. & Granger, C.W.J. (2003). Forecasting Volatility in Financial Markets: A Review, J. of Economic Literature, 41, 478–539 Poon, W.P.H. & Shen, J. (2020). The roles of rating outlooks: the predictor of creditworthiness and the monitor of recovery efforts. Rev.Quant.Finan.Acc., (2020). https://doi.org/10.1007/s11156019008687 Stigler, G.J., & Kindahl, J.K. (1970). The Dispersion of Price Movements, in Ed. Stigler,G.J. & Kindahl, J.K. The Behavior of Industrial Prices, NBER, 88  94 Schuermann, T. & Jafry, Y. (2003). Measurement and Estimation of Credit Migration Matrices, The Wharton Financial Institutions Center, 144 Schwert, G.W. (1988). Why Does Stock Market Volatility Change Over Time? NBER WP 2798 S&P, (2014). Guide To Credit Rating Essentials. What are credit ratings and how do they work? McGraw Hill Financial S&P&, (2016). S&P Global Ratings Definitions. S&P Global Ratings S&P, (2018). 2018 Annual Global Corporate Default And Rating Transition Study Takaishi, T. & Chen, T. T. (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. & Pitts, M. (1983). The Price VariabilityVolume Relationship On Speculative Markets, Econometrica, 51, (2), 485505 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/107316 
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Price, Volatility and the SecondOrder Economic Theory. (deposited 09 Sep 2020 15:36)

Price, Volatility and the SecondOrder Economic Theory. (deposited 09 Oct 2020 11:22)
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Price, Volatility and the SecondOrder Economic Theory. (deposited 09 Oct 2020 11:22)