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Three Remarks On Asset Pricing

Olkhov, Victor (2022): Three Remarks On Asset Pricing.

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We consider well-known consumption-based asset pricing theory and regard the choice of the time interval Δ used for averaging the market price time-series 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 n-th statistical moments p(t;n) as generalization of the well-known definition of volume weighted average price (VWAP). We demonstrate that usage of VWAP causes zero correlations between price and trade volume. Usage of price n-th statistical moments causes zero correlations between n-th 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 market-based price probability at horizon T should match forecasts of finite number of n-th statistical moments of the trade value C(t;n) and volume U(t;n) at the same horizon T. The new definition of the market-based asset price probability emphasizes its direct dependence on random properties of the market trade.

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