Association or interdependence of two stock prices is analyzed, and selection criteria for a suitable model developed in the present paper. The association is generated by stochastic correlation, given by a stochastic differential equation (SDE), creating interdependent Wiener processes. These, in turn, drive the SDEs in the Heston model for stock prices. To choose from possible stochastic correlation models, two goodness-of-fit procedures are proposed based on the copula of Wiener increments. One uses the confidence domain for the centered Kendall function, and the other relies on strong and weak tail dependence. The constant correlation model and two different stochastic correlation models, given by Jacobi and hyperbolic tangent transformation of Ornstein-Uhlenbeck (HtanOU) processes, are compared by analyzing daily close prices for Apple and Microsoft stocks. The constant correlation, i.e., the Gaussian copula model, is unanimously rejected by the methods, but all other two are acceptable at a 95% confidence level. The analysis also reveals that even for Wiener processes, stochastic correlation can create tail dependence, unlike constant correlation, which results in multivariate normal distributions and hence zero tail dependence. Hence models with stochastic correlation are suitable to describe more dangerous situations in terms of correlation risk.

分析了两种股票价格的关联或相互依赖性，并为本文开发了合适​​的模型而选择了标准。关联是通过随机相关性生成的，由随机微分方程（SDE）给出，从而创建相互依赖的维纳过程。这些反过来推动了Heston模型中股票价格的SDE。为了从可能的随机相关模型中进行选择，基于维纳增量的copula提出了两种拟合优度程序。一种将置信域用于居中的Kendall函数，另一种依赖于强尾依赖关系。常数相关模型和两种不同的随机相关模型，分别由Jacobi和Ornstein-Uhlenbeck（HtanOU）过程的双曲正切变换给出，通过分析苹果和微软股票的每日收盘价进行比较。该方法一致拒绝了常数相关性，即高斯copula模型，但是在95％的置信度下，所有其他两个都是可以接受的。分析还表明，即使对于维纳过程，随机相关也会产生尾部相关性，这与恒定相关性不同，后者会导致多元正态分布，因此零尾部相关性。因此，具有随机相关性的模型适合于用相关性风险描述更危险的情况。与常数相关不同，随机相关会产生尾部相关性，而常数相关性会导致多元正态分布，因此尾部相关性为零。因此，具有随机相关性的模型适合于用相关性风险描述更危险的情况。与常数相关不同，随机相关会产生尾部相关性，而常数相关性会导致多元正态分布，因此尾部相关性为零。因此，具有随机相关性的模型适合于用相关性风险描述更危险的情况。