Market-Based Asset Price Probability

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

Abstract

We consider the randomness of market trade values and volumes as the origin of asset price stochasticity. We define the first four market-based price statistical moments that depend on statistical moments and correlations of market trade values and volumes. Market-based price statistical moments coincide with conventional frequency-based ones if all trade volumes are constant during the time averaging interval. We present approximations of market-based price probability by a finite number of price statistical moments. We consider the consequences of the use of market-based price statistical moments for asset-pricing models and Value-at-Risk. We show that the use of volume weighted average price results in zero price-volume correlations. We derive market-based correlations between price and squares of volume and between squares of price and volume. To forecast market-based price volatility at horizon T one should predict the first two statistical moments of market trade values and volumes and their correlations at the same horizon T.

• 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

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, (2005). Volatility Forecasting, CFS WP 2005/08, 1-116

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

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

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

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

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

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

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

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

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., (2021b), Three Remarks On Asset Pricing, SSRN WP3852261, 1-24.

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

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

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