Olkhov, Victor (2022): Three Remarks On Asset Pricing.
This is the latest version of this item.

PDF
MPRA_paper_114185.pdf Download (255kB)  Preview 
Abstract
We consider wellknown consumptionbased asset pricing theory and regard the choice of the time interval Δ used for averaging the market price timeseries as the key factor of asset pricing. We show that the explicit usage of the averaging interval Δ allows expand investor’s utility into Taylor series and derive successive approximations of the basic asset pricing equation. For linear and quadratic Taylor series approximations of the basic pricing equation we derive new expressions of the mean price, mean payoff, their volatilities, skewness and amount of asset ξmax that delivers max to investor’s utility. The treatment of the market price as a coefficient between the trade value and volume prohibits independent definition of the trade value, volume and price probabilities. We introduce price nth statistical moments p(t;n) as generalization of the wellknown definition of volume weighted average price (VWAP). We demonstrate that usage of VWAP causes zero correlations between price and trade volume. Usage of price nth statistical moments causes zero correlations between nth power of price pn and trade volume Un, but don’t causes statistical independence. As example, we derive expression for correlation between price p and squares of trade volume U2. Any predictions of the marketbased price probability at horizon T should match forecasts of finite number of nth statistical moments of the trade value C(t;n) and volume U(t;n) at the same horizon T. The new definition of the marketbased asset price probability emphasizes its direct dependence on random properties of the market trade.
Item Type:  MPRA Paper 

Original Title:  Three Remarks On Asset Pricing 
English Title:  Three Remarks On Asset Pricing 
Language:  English 
Keywords:  asset pricing, volatility, price probability, market trades 
Subjects:  C  Mathematical and Quantitative Methods > C0  General > C02  Mathematical Methods D  Microeconomics > D4  Market Structure, Pricing, and Design > D40  General D  Microeconomics > D5  General Equilibrium and Disequilibrium > D53  Financial Markets G  Financial Economics > G1  General Financial Markets > G10  General G  Financial Economics > G1  General Financial Markets > G12  Asset Pricing ; Trading Volume ; Bond Interest Rates 
Item ID:  114185 
Depositing User:  Victor Olkhov 
Date Deposited:  15 Aug 2022 00:17 
Last Modified:  15 Aug 2022 00:17 
References:  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., Diebold, F.X. (2005). Volatility Forecasting, CFS WP 2005/08, 1116 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 Borovička, J., Hansen, L.P. (2012). Examining Macroeconomic Models through the Lens of Asset Pricing. FRB Chicago Brock, W.A., LeBaron, B.D. (1995). A Dynamic structural model for stock return volatility and trading volume. NBER, WP 4988, 146 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., Shiller, R.J. (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 CME Group (2020) https://www.cmegroup.com/search.html?q=VWAP Cochrane, J.H., Hansen, L.P.: Asset Pricing Explorations for Macroeconomics. Ed., Blanchard, O.J., Fischer, S. (1992). NBER Macroeconomics Annual 1992, v. 7, 115 – 182 Cochrane, J.H. (2001). Asset Pricing. Princeton Univ. Press, Princeton, US Cochrane, J.H., Culp, C.L. (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 Cochrane, J.H. (2021). Portfolios For LongTerm Investors. NBER, WP28513, 154 DeFusco, A.A., Nathanson, C.G. and E. Zwick, (2017). Speculative Dynamics of Prices and Volume, Cambridge, MA, NBER WP 23449, 174 Duffie, D., Dworczak, P. (2018). Robust Benchmark Design. NBER, WP 20540, 156 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 Ferson, W.E., Sarkissian, S., Simin, T. (1999). The alpha factor asset pricing model: A parable. J. Financial Markets, 2, 4968 Forbes, C., Evans, M., Hastings, N., Peacock, B. (2011). Statistical Distributions. Wiley 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., Lipsey, R.E. (1963). Asset Prices and the General Price Level, NBER, 166 – 189, in National Balance Sheet of the United States, Ed. Goldsmith, R.W. and R. E. Lipsey Greenwood, R., Shleifer, A. (2014). Expectations of Returns and Expected Returns. The Review of Financial Studies, 27 (3), 714–746 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) Heaton, J., Lucas, D. (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., Packer, F. (2007). Understanding asset prices: an overview. Bank for International Settlements, WP 34, 138 Karpoff, J.M. (1987). The Relation Between Price Changes and Trading Volume: A Survey. The Journal of Financial and Quantitative Analysis, 22 (1), 109126 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 Llorente, G., Michaely R., Saar, G. and J. Wang. (2001). Dynamic VolumeReturn Relation of Individual Stocks. NBER, WP 8312, Cambridge, MA., 155 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 Mackey, M.C. (1989). Commodity Price Fluctuations: Price Dependent Delays and Nonlinearities as Explanatory Factors. J. Economic Theory, 48, 497509 Malkiel, B., Cragg, J.G. (1980). Expectations and valuations of shares. NBER, WP 471 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 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, 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 Perold, A.F. (2004). The Capital Asset Pricing Model. J. Economic Perspectives, 18(3), 3–24 Poon, SH., Granger, C.W.J. (2003). Forecasting Volatility in Financial Markets: A Review, J. of Economic Literature, 41, 478–539 Schwert, G. (1988). Why Does Stock Market Volatility Change Over Time? NBER WP2798 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 Stigler, G.J, Kindahl, J.K. (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., Pitts, M. (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 Xu, J. (2007). Price Convexity and Skewness. Jour of Finance, 67 (5), 25212552 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/114185 