The Market-Based Asset Price Probability

Olkhov, Victor (2022): The Market-Based Asset Price Probability.

Abstract

This paper introduces the market-based asset price probability during time averaging interval Δ. We substitute the present problem of guessing the “correct” form of the asset price probability by description of the price probability as function of the market trade value and volume statistical moments during Δ. We define n-th price statistical moments as ratio of n-th statistical moments of the trade value to n-th statistical moments of the trade volume. That definition states no correlations between time-series of n-th power of the trade volume and price during Δ, but doesn’t result statistical independence between the trade volume and price. The set of price n-th statistical moments defines Taylor series of the price characteristic function. Approximations of the price characteristic function that reproduce only first m price statistical moments, generate approximations of the market-based price probability. That approach unifies probability description of market-based asset price, price indices, returns, inflation and their volatilities. Market-based price probability approach impacts the asset pricing models and uncovers hidden troubles and usage bounds of the widespread risk hedging tool – Value-at-Risk, lets you determine the price autocorrelations and revises the classical option pricing from one to two dimensional problem. Market-based approach doesn’t simplify the price probability puzzle but establishes direct economic ties between asset pricing, market randomness and economic theory. Description of the market-based price and returns volatility, Skewness and Kurtosis requires development of economic theories those model relations between second, third and forth order macroeconomic variables. Development of these theories will take a lot of efforts and years.

• Item Type: MPRA Paper
• 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

References

Anderson, T.W. (1971). The Statistical Analysis of Time-Series. Wiley&.Sons, Inc., 1-757

Andersen, T., Bollerslev, T., Diebold, F.X, Ebens, H. (2001). The Distribution of Realized Stock Return Volatility, Journal of Financial Economics, 61, 43-76

Andersen, T.G, Bollerslev, T., Christoffersen, P.F. and F.X. Diebold, (2005a). Volatility Forecasting, CFS WP 2005/08, 1-116

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, 1-41

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: North-Holland, 778-878

Bachelier, L., (1900). Théorie de la speculation, Annales scientifiques de l’É.N.S. 3e série, 17, 21-86

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), 97-112

Black, F. and M. Scholes, (1973). The Pricing of Options and Corporate Liabilities, J. Political Economy, 81 (3), 637-654

Bogousslavsky, V. and P. Collin-Dufresne, (2019). Liquidity, Volume, and Volatility, Swiss Finance Institute, RPS 19-69, 1-59

Brock, W.A. and B.D. LeBaron, (1995). A Dynamic structural model for stock return volatility and trading volume. NBER, WP 4988, 1-46

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, 1-34, arXiv:1509.08503v1

Campbell, J.Y. and R.J. Shiller, (1988). Stock Prices, Earnings And Expected Dividends. NBER, WP 2511, 1-42

Campbell, J.Y., Grossman, S.J. and J.Wang, (1993). Trading Volume and Serial Correlation in Stock Return. Quatr. Jour. Economics, 108 (4), 905-939

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), 1515-1567

Campbell, J.Y. (2002). Consumption-Based Asset Pricing. Harvard Univ., Cambridge, Discussion Paper # 1974, 1-116

Choudhry, M., (2013). An Introduction to Value-at-Risk, 5th Edition. Wiley, 1-224

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, 1-136

Cochrane, J.H. (2022). Portfolios For Long-Term Investors, Rev. Finance, 26(1), 1–42

CreditMetrics™, (1997). Technical Document. J.P. Morgan & Co, NY. 1-212

Davis, H.T., (1941). The Analysis of Economic Time-Series. Cowles Commission for Research in Economics. The Principia Press, Inc., 1-627

DeFusco, A.A., Nathanson, C.G. and E. Zwick, (2017). Speculative Dynamics of Prices and Volume, Cambridge, MA, NBER WP 23449, 1-74

Diebold, F.X. and K. Yilmaz, (2008). Macroeconomic Volatility And Stock Market Volatility, Worldwide, NBER WP 14269, 1-35

Diebold, F.X. (2019). Time Series Econometrics, Univ. Pennsylvania, 1-215

Dimson. E. and M.Mussavian, (1999). Three centuries of asset pricing. J.Banking&Finance, 23(12) 1745-1769

Duffie, D., Dworczak, P. (2021). Robust Benchmark Design. Journal of Financial Economics, 142(2), 775–802

Fama, E.F. (1965). The Behavior of Stock-Market Prices. J. Business, 38 (1), 34-105

Fama, E.F. and K.R. French, (2015). A five-factor asset pricing model. J. Financial Economics, 116, 1-22

Fetter, F.A., (1912). The Definition of Price. American Economic Rev., 2 (4), 783-813

Forbes, C., Evans, M., Hastings, N., Peacock, B. (2011). Statistical Distributions. Wiley

Friedman, D.D. (1990). Price Theory: An Intermediate Text. South-Western Pub. Co., US

Gallant, A.R., Rossi, P.E. and G. Tauchen, (1992). Stock Prices and Volume, The Review of Financial Studies, 5(2), 199-242

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, 1-38

Ito, T. and W.L. Lin, (1993). Price Volatility And Volume Spillovers Between The Tokyo And New York Stock Markets, NBER WP 4592, 1-35

Karpoff, J.M. (1987). The Relation Between Price Changes and Trading Volume: A Survey. The Journal of Financial and Quantitative Analysis, 22 (1), 109-126

Kendall, M.G and A.B. Hill, (1953). The Analysis of Economic Time-Series-Part I: Prices. Jour. Royal Statistical Soc., Series A, 116 (1), 11-34

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 Volume-Return Relation of Individual Stocks. NBER, WP 8312, Cambridge, MA., 1-55

Longerstaey, J., and M. Spencer, (1996). RiskMetrics -Technical Document. J.P.Morgan & Reuters, N.Y., Fourth Edition, 1-296

Mackey, M.C. (1989). Commodity Price Fluctuations: Price Dependent Delays and Nonlinearities as Explanatory Factors. J. Economic Theory, 48, 497-509

Malkiel, B. and J.G. Cragg, (1980). Expectations and the valuations of shares, NBER WP 471, 1-70

Mandelbrot. B, Fisher, A. and L. Calvet, (1997). A Multifractal Model of Asset Returns, Yale University, Cowles Foundation Discussion WP1164, 1-39

Merton, R.C. (1973). An Intertemporal Capital Asset Pricing Model, Econometrica, 41, (5), 867-887

Mills, F.C. (1946). Price-Quantity Interactions in Business Cycles. NBER, Prins.Univ., NY

Muth, J.F. (1961). Rational Expectations and the Theory of Price Movements, Econometrica, 29, (3) 315-335

Olkhov, V. (2020). Volatility Depend on Market Trades and Macro Theory. MPRA, WP102434, 1-18

Olkhov, V. (2021a). Price, Volatility and the Second-Order Economic Theory. ACRN Jour. Finance & Risk Perspectives, Sp. Issue, 18th FRAP Conference, 10, 139-165

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, 1-16

Olkhov, V., (2021d), Three Remarks On Asset Pricing, SSRN WP 3852261, 1-24.

Olkhov, V. (2021e). Theoretical Economics and the Second-Order Economic Theory. What is it? SSRN, WP 3975585, 1-14

Olkhov, V. (2022a). Price and Payoff Autocorrelations in the Consumption-Based Asset Pricing Model, SSRN, WP 4050652, 1- 18

Olkhov, V. (2022b). Introduction of the Market-Based Price Autocorrelation, SSRN, WP 4035874, 1-13

Olkhov, V. (2022c). Economic Policy - The Forth Dimension of the Economic Theory, SSRN, WP 4079069, 1-20

Odean,T. (1998). Volume, Volatility, Price, And Profit When All Traders Are Above Average, The Journal of Finance, LIII, (6), 1887-1934

Papoulis, A. and S.U. Pillai, (2002). Probability Random Variables and Stochastic Processes, 4th Ed., McGraw-Hill, NY.,1-860

Poon, S-H. 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), 425-442

Shephard, N.G. (1991). From Characteristic Function to Distribution Function: A Simple Framework for the Theory. Econometric Theory, 7 (4), 519-529

Shiryaev, A.N. (1999). Essentials Of Stochastic Finance: Facts, Models, Theory. World Sc. Pub., Singapore. 1-852

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 Variability-Volume Relationship On Speculative Markets, Econometrica, 51, (2), 485-505

Walck, C. (2011). Hand-book 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, 1-22