Three Remarks On Asset Pricing

Abstract

The consideration of an averaging interval Δ of market trade time-series change the basic consumption-based asset pricing equation. The duration of Δ determines Taylor series of investor’s utility over current and future values of consumption. We present consumption at current and future moments as sums of their mean values and perturbations during Δ of the price at current moment t and perturbations of the payoff at day t+1. Linear and quadratic Taylor series approximations of the basic equation describe new relations on mean price, mean payoff, their volatilities, skewness and amount of asset ξmax that delivers max to investor’s utility. The stochasticity of market trade time-series defines the randomness of the asset price. We introduce the new price probability measure entirely determined by the probability measures of market trade value and volume. The conventional frequency-based price probability is a special case of the new price probability measure when all trade volumes during the averaging interval Δ equal unit. Prediction of the price probability measure at horizon T equals forecasts of the market trade value and volume probabilities at same horizon.