论文标题
价格，波动性和二阶经济理论
Price, Volatility and the Second-Order Economic Theory
论文作者
论文摘要
我们介绍了定义平均价格p（1; t），平均价格p（2; t），价格波动量σp2（t）和所有价格n-统计矩p（n; t）为n-度量值c（n; t）的总和（n; t）在某些时间差异的情况下，定义了价格p（2; t），所有价格n-统计矩p（n; t）的比率，在某些时间tripe timece中，我们介绍了平均价格p（1; t），均值p（2; t），价格波动σp2（t）和所有价格n-度量值c（n; t）和某些时间差异的时间范围的时间n-平均价格p（1; t）的定义与至少30年前引入的体积加权平均价格（VWAP）的定义一致。我们表明，价格波动σp2（t）的预测需要建模二级值C（2; t）和体积u（2; t）的总和的演变。我们将此模型称为二阶经济理论。我们使用数值连续风险评级作为对经济代理的风险评估，并通过风险评级作为坐标来分配代理。我们引入了持续的经济媒体近似值的近似值和体积的量和它们在时间间隔δ期间聚集的流量。我们考虑了管理代理商进行交易的期望，并引入了汇总期望，以汇总交易。我们得出了在二级交易上连续经济媒体近似的方程式。在线性近似中，我们得出均方而一的平方价P（2; t）和波动率σp2（t）干扰，作为一级和二级交易的函数。对单位价格度量η（p; t）的每个n-the Price统计矩P（n; t）的描述取决于n-度值c（n; t）的总和c（n; t）和市场交易的体积u（n; t），因此需要发展相应的n阶经济理论。
We introduce the price probability measure η(p;t) that defines the mean price p(1;t), mean square price p(2;t), price volatility σp2(t)and all price n-th statistical moments p(n;t) as ratio of sums of n-th degree values C(n;t) and volumes U(n;t) of market trades aggregated during certain time interval Δ. The definition of the mean price p(1;t) coincides with definition of the volume weighted average price (VWAP) introduced at least 30 years ago. We show that price volatility σp2(t) forecasting requires modeling evolution of the sums of second-degree values C(2;t) and volumes U(2;t). We call this model as second-order economic theory. We use numerical continuous risk ratings as ground for risk assessment of economic agents and distribute agents by risk ratings as coordinates. We introduce continuous economic media approximation of squares of values and volumes of agents trades and their flows aggregated during time interval Δ. We take into account expectations that govern agents trades and introduce aggregated expectations alike to aggregated trades. We derive equations for continuous economic media approximation on the second-degree trades. In the linear approximation we derive mean square price p(2;t) and volatility σp2(t) disturbances as functions of the first and second-degree trades disturbances. Description of each next n-th price statistical moment p(n;t) with respect to the unit price measure η(p;t) depends on sums of n-th degree values C(n;t) and volumes U(n;t) of market trades and hence requires development of the corresponding n-th order economic theory.
