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The Market-Based Asset Price Probability

Olkhov, Victor (2022): The Market-Based 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 market-based 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 well-known definition of the volume weighted average price (VWAP) presented more than 30 years ago and introduce market price n-th statistical moments as n-th power volume weighted average. That results in zero correlations between time-series of n-th 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 time-series 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 market-based price probability. That approach unifies description of the asset price, price indices, returns, inflation and their volatilities. Market-based approach impacts the asset pricing models and uncovers hidden vital fault of the widely used hedging tool – Value-at-Risk. 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 market-based 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.

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