资产定价核还原方法的算符表述及其应用--以中国股票市场泡沫诊断为例

The Recovery Approach Based on State Transition Pricing Operator Application to the Diagnosing of Bubbles in China Stock Market

传统金融工程技术能够得到风险中性概率,但如果不还原出表征市场风险偏好结构的定价核,无法进一步得到真实概率。围绕定价核的还原研究,近年来出现两类不同的方法：Ross的矩阵法,Carr和Yu的微分方程法。前者求解矩阵最大特征值,后者求解方程最小特征值。本文通过引入状态转移定价算符,探讨这两种方法的内在联系,给出统一表述的还原法：求解定价算符特征方程,其最大实特征值对应市场贴现率,而特征函数代表各状态下的基准风险溢价水平。作为应用,本文研究了我国2005-2007年股市泡沫下的定价核,估计出各行业的风险补偿和贴现要求,证实了泡沫过程中货币幻觉存在性。

Conventional financial engineering technique only helps one to estimate risk-neutral probability. However,it is impossible to further obtain natural probability without recovering pricing kernel that reflecting the structure of risk aversion preference for the overall market. At present,two kinds of major approaches to recovery pricing kernel are presented,which are respectively matrix-based-method from Ross and differential equation method derived in Carr and Yu.The former relies on finding out the maximum eigenvalue,whereas the later works by searching the minimum eigenvalue.This paper discusses the internal relation-ship between these two kinds of approaches. By introducing the state transition pricing operator,the current two approaches can be uniformed to solve the operator eigenvalue equation,which eigenvalues and eigen-functions respectively indicate the inter-temporal discount rate and the required numeraire risk premium.As an application,the performance of stock bubbles for China between 2005 and 2007 is diagnosed. Except for estimating the risk compensation in different industry,we also confirm the presence of money illusion characterized by distorted discount rate.