Abstract Convergence models of interest rates are used to model a situation, where a country is going to enter a monetary union and its short rate is affected by the short rate in the monetary union. In addition, Wiener processes which model random shocks in the behaviour of the short rates can be correlated. In this paper we consider a stochastic correlation in a selected convergence model. A stochastic correlation has been already studied in different contexts in financial mathematics, therefore we distinguish differences which come from modelling interest rates by a convergence model. We provide meaningful properties which a correlation model should satisfy and afterwards we study the problem of solving the partial differential equation for the bond prices. We find its solution in a separable form, where the term coming from the stochastic correlation is given in its series expansion for a high value of the correlation.

中文翻译：

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具有随机相关性的利率收敛模型中的债券定价偏微分方程

摘要 利率收敛模型用于模拟一种情况，即一国将加入货币联盟，其短期利率受货币联盟短期利率的影响。此外，对短期利率行为中的随机冲击进行建模的维纳过程可以相关联。在本文中，我们考虑所选收敛模型中的随机相关性。已经在金融数学的不同背景下研究了随机相关性，因此我们通过收敛模型区分来自建模利率的差异。我们提供相关模型应该满足的有意义的属性，然后我们研究求解债券价格的偏微分方程的问题。我们以可分离的形式找到它的解，