  We consider the consumption-based asset pricing model, derive a new modified
basic pricing equation, and present its successive approximations using the
Taylor series expansions of the investor's utility during the averaging time
interval. For linear and quadratic Taylor approximations, we derive new
expressions for the mean price, mean payoff, volatility, skewness, and the
asset's amount that define the maximum of the investor's utility. We discuss
the market-based origin of price probability. We use volume weighted average
price (VWAP) as a market-based average price and introduce market-based price
volatility. The use of VWAP results in zero correlations between the price p
and trade volume U. We derive a correlation between price p and squares of
trade volume {U^2} and between squares of price {p^2} and volume {U^2}. To
predict market-based price volatility, one should forecast the 2-d statistical
moments of the market trade values and volumes at the same horizon T.
