Olkhov, Victor (2022): The MarketBased Asset Price Probability.
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Abstract
This paper considers asset price as a random variable during the averaging interval Δ and introduces the marketbased price probability. We substitute the problem of guessing the “correct” form of the asset price probability by approximate description of random price properties by the finite number of price statistical moments determined by statistical moments of the market trade value and volume during Δ. We extend the wellknown definition of the volume weighted average price (VWAP) presented more than 30 years ago and introduce market price nth statistical moments as nth power volume weighted average. That results in zero correlations between timeseries of nth power of the trade volume and price during Δ, but doesn’t cause statistical independence between trade volume and price. As example we derive expression for correlation between timeseries of the market price and squares of the trade volume. The market trades records during Δ allow assess only finite number of statistical moments. Approximations of the price characteristic function that reproduce first m price statistical moments generate approximations of the marketbased price probability. That approach unifies description of the asset price, price indices, returns, inflation and their volatilities. Marketbased approach impacts the asset pricing models and uncovers hidden vital fault of the widely used hedging tool – ValueatRisk. Our approach doesn’t simplify the random price puzzle but establishes direct economic ties and relations between asset pricing, market stochasticity and economic theory. Description of the marketbased price and returns volatility, Skewness and Kurtosis requires development of the economic theories those model relations between the second, third and forth order macroeconomic variables. Development of these theories will take a lot of efforts and years.
Item Type:  MPRA Paper 

Original Title:  The MarketBased Asset Price Probability 
English Title:  The MarketBased Asset Price Probability 
Language:  English 
Keywords:  asset price; price probability; returns; inflation; market trades 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics C  Mathematical and Quantitative Methods > C5  Econometric Modeling > C58  Financial Econometrics E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E31  Price Level ; Inflation ; Deflation E  Macroeconomics and Monetary Economics > E3  Prices, Business Fluctuations, and Cycles > E37  Forecasting and Simulation: Models and Applications 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:  114186 
Depositing User:  Victor Olkhov 
Date Deposited:  15 Aug 2022 02:23 
Last Modified:  15 Aug 2022 02:23 
References:  Anderson, T.W. (1971). The Statistical Analysis of TimeSeries. Wiley&.Sons, Inc., 1757 Andersen, T., Bollerslev, T., Diebold, F.X, Ebens, H. (2001). The Distribution of Realized Stock Return Volatility, Journal of Financial Economics, 61, 4376 Andersen, T.G, Bollerslev, T., Christoffersen, P.F. and F.X. Diebold, (2005a). Volatility Forecasting, CFS WP 2005/08, 1116 Andersen, T.G., Bollerslev, T., Christoffersen, P.F. and F.X. Diebold, (2005b). Practical Volatility And Correlation Modelling For Financial Market Risk Management, NBER, WP11069, Cambridge, MA, 141 Andersen, T.G., Bollerslev, T., Christoffersen, P.F., and Diebold, F.X. (2006). Volatility and Correlation Forecasting, in G. Elliot, C.W.J. Granger, and Allan Timmermann (eds.), Handbook of Economic Forecasting. Amsterdam: NorthHolland, 778878 Bachelier, L., (1900). Théorie de la speculation, Annales scientifiques de l’É.N.S. 3e série, 17, 2186 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 Black, F. and M. Scholes, (1973). The Pricing of Options and Corporate Liabilities, J. Political Economy, 81 (3), 637654 Bogousslavsky, V. and P. CollinDufresne, (2019). Liquidity, Volume, and Volatility, Swiss Finance Institute, RPS 1969, 159 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 Campbell, J.Y. and R.J. Shiller, (1988). Stock Prices, Earnings And Expected Dividends. NBER, WP 2511, 142 Campbell, J.Y., Grossman, S.J. and J.Wang, (1993). Trading Volume and Serial Correlation in Stock Return. Quatr. Jour. Economics, 108 (4), 905939 Campbell, J.Y. (1998). Asset Prices, Consumption, and the Business Cycle. NBER, WP6485 Campbell, J.Y. (2000). Asset Pricing at the Millennium. Jour. of Finance, 55(4), 15151567 Campbell, J.Y. (2002). ConsumptionBased Asset Pricing. Harvard Univ., Cambridge, Discussion Paper # 1974, 1116 Choudhry, M., (2013). An Introduction to ValueatRisk, 5th Edition. Wiley, 1224 Ciner, C. and W. H. Sackley, (2007). Transactions, volume and volatility: evidence from an emerging market, Applied Financial Economics Letters, 3, 161–164 CME Group, (2020). https://www.cmegroup.com/search.html?q=VWAP Cochrane, J.H. and L.P. Hansen, (1992). Asset Pricing Explorations for Macroeconomics. Ed., Blanchard, O.J., Fischer, S. NBER Macroeconomics Annual 1992, v. 7, 115 – 182 Cochrane, J.H. (2001). Asset Pricing. Princeton Univ. Press, Princeton, US Cochrane, J.H. (2005). Time Series for Macroeconomics and Finance. Graduate School of Business, Univ. Chicago, 1136 Cochrane, J.H. (2022). Portfolios For LongTerm Investors, Rev. Finance, 26(1), 1–42 CreditMetrics™, (1997). Technical Document. J.P. Morgan & Co, NY. 1212 Davis, H.T., (1941). The Analysis of Economic TimeSeries. Cowles Commission for Research in Economics. The Principia Press, Inc., 1627 DeFusco, A.A., Nathanson, C.G. and E. Zwick, (2017). Speculative Dynamics of Prices and Volume, Cambridge, MA, NBER WP 23449, 174 Diebold, F.X. and K. Yilmaz, (2008). Macroeconomic Volatility And Stock Market Volatility, Worldwide, NBER WP 14269, 135 Diebold, F.X. (2019). Time Series Econometrics, Univ. Pennsylvania, 1215 Dimson. E. and M.Mussavian, (1999). Three centuries of asset pricing. J.Banking&Finance, 23(12) 17451769 Duffie, D., Dworczak, P. (2021). Robust Benchmark Design. Journal of Financial Economics, 142(2), 775–802 Fama, E.F. (1965). The Behavior of StockMarket Prices. J. Business, 38 (1), 34105 Fama, E.F. and K.R. French, (2015). A fivefactor asset pricing model. J. Financial Economics, 116, 122 Fetter, F.A., (1912). The Definition of Price. American Economic Rev., 2 (4), 783813 Forbes, C., Evans, M., Hastings, N., Peacock, B. (2011). Statistical Distributions. Wiley Fox, D.R. et al. (2017). Concepts and Methods of the U.S. National Income and Product Accounts. BEA, US.Dep. Commerce, 1447 Friedman, D.D. (1990). Price Theory: An Intermediate Text. SouthWestern Pub. Co., US Gallant, A.R., Rossi, P.E. and G. Tauchen, (1992). Stock Prices and Volume, The Review of Financial Studies, 5(2), 199242 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 Greenwood, R. and A. Shleifer, (2014). Expectations of Returns and Expected Returns. The Review of Financial Studies, 27 (3), 714–746 Heaton, J. and D. Lucas, (2000). Stock Prices and Fundamentals. Ed. Ben S. Bernanke, B.S and J. J. Rotemberg, NBER Macroeconomics Annual 1999, v. 14., 213 – 264 Hördahl, P. and F. Packer, (2007). Understanding asset prices: an overview. Bank for International Settlements, WP 34, 138 Ito, T. and W.L. Lin, (1993). Price Volatility And Volume Spillovers Between The Tokyo And New York Stock Markets, NBER WP 4592, 135 Karpoff, J.M. (1987). The Relation Between Price Changes and Trading Volume: A Survey. The Journal of Financial and Quantitative Analysis, 22 (1), 109126 Kendall, M.G and A.B. Hill, (1953). The Analysis of Economic TimeSeriesPart I: Prices. Jour. Royal Statistical Soc., Series A, 116 (1), 1134 Klyatskin, V.I. (2005). Stochastic Equations through the Eye of the Physicist, Elsevier B.V. Llorente, G., Michaely R., Saar, G. and J. Wang. (2001). Dynamic VolumeReturn Relation of Individual Stocks. NBER, WP 8312, Cambridge, MA., 155 Longerstaey, J., and M. Spencer, (1996). RiskMetrics Technical Document. J.P.Morgan & Reuters, N.Y., Fourth Edition, 1296 Mackey, M.C. (1989). Commodity Price Fluctuations: Price Dependent Delays and Nonlinearities as Explanatory Factors. J. Economic Theory, 48, 497509 Malkiel, B. and J.G. Cragg, (1980). Expectations and the valuations of shares, NBER WP 471, 170 Mandelbrot. B, Fisher, A. and L. Calvet, (1997). A Multifractal Model of Asset Returns, Yale University, Cowles Foundation Discussion WP1164, 139 Merton, R.C. (1973). An Intertemporal Capital Asset Pricing Model, Econometrica, 41, (5), 867887 Mills, F.C. (1946). PriceQuantity Interactions in Business Cycles. NBER, Prins.Univ., NY Muth, J.F. (1961). Rational Expectations and the Theory of Price Movements, Econometrica, 29, (3) 315335 Olkhov, V. (2020). Volatility Depend on Market Trades and Macro Theory. MPRA, WP102434, 118 Olkhov, V. (2021a). Price, Volatility and the SecondOrder Economic Theory. ACRN Jour. Finance & Risk Perspectives, Sp. Issue, 18th FRAP Conference, 10, 139165 Olkhov, V. (2021b). To VaR, or Not to VaR, That is the Question. SSRN, WP 3770615 Olkhov, V. (2021c). Classical Option Pricing and Some Steps Further, SSRN, WP 3587369, 116 Olkhov, V., (2021d), Three Remarks On Asset Pricing, SSRN WP 3852261, 124.\ Olkhov, V. (2021e). Theoretical Economics and the SecondOrder Economic Theory. What is it? SSRN, WP 3975585, 114 Olkhov, V. (2022a). Price and Payoff Autocorrelations in the ConsumptionBased Asset Pricing Model, SSRN, WP 4050652, 1 18 Olkhov, V. (2022b). Introduction of the MarketBased Price Autocorrelation, SSRN, WP 4035874, 113 Olkhov, V. (2022c). Economic Policy  The Forth Dimension of the Economic Theory, SSRN, WP 4079069, 120 Odean,T. (1998). Volume, Volatility, Price, And Profit When All Traders Are Above Average, The Journal of Finance, LIII, (6), 18871934 Papoulis, A. and S.U. Pillai, (2002). Probability Random Variables and Stochastic Processes, 4th Ed., McGrawHill, NY.,1860 Poon, SH. and C.W.J. Granger, (2003). Forecasting Volatility in Financial Markets: A Review, J. of Economic Literature, 41, 478–539 Sharpe, W.F. (1964). Capital Asset Prices: A Theory of Market Equilibrium under Conditions of Risk. The Journal of Finance, 19 (3), 425442 Shephard, N.G. (1991). From Characteristic Function to Distribution Function: A Simple Framework for the Theory. Econometric Theory, 7 (4), 519529 Shiryaev, A.N. (1999). Essentials Of Stochastic Finance: Facts, Models, Theory. World Sc. Pub., Singapore. 1852 Shreve, S. E. (2004). Stochastic calculus for finance, Springer finance series, NY, USA Stigler, G.J. and J.K. Kindahl, (1970). The Dispersion of Price Movements, NBER, 88  94 in Ed. Stigler, G.J, Kindahl, J.K. The Behavior of Industrial Prices Tauchen, G.E. and M. Pitts, (1983). The Price VariabilityVolume Relationship On Speculative Markets, Econometrica, 51, (2), 485505 Walck, C. (2011). Handbook on statistical distributions. Univ.Stockholm, SUF–PFY/96–01 Weyl, E.G. (2019). Price Theory, AEA J. of Economic Literature, 57(2), 329–384 Wolfers, J. and E. Zitzewitz, (2006). Interpreting Prediction Market Prices As Probabilities, NBER WP12200, 122 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/114186 
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