We study the valuation of callable barrier reverse convertible contracts written on one or two underlying asset prices. We assume the issuer of the contract can call early redemption at any time during a pre-specified time interval. We identify the optimal redemption policy and show, in the single underlying asset case, it is characterized by a time-dependent boundary. The boundary satisfies a nonlinear integral equation of the Volterra type. When there are two underlying assets, the boundary is a surface depending on one price in addition to time. Valuation formulas and associated integral equations are derived. Numerical experiments are performed.

中文翻译：

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可赎回障碍反向可转换证券

我们研究了以一两个标的资产价格编写的可赎回障碍反向转换合约的估值。我们假设合约的发行者可以在预先指定的时间间隔内随时调用提前赎回。我们确定了最佳赎回政策，并表明，在单一标的资产情况下，它的特点是时间相关的边界。边界满足 Volterra 类型的非线性积分方程。当有两个标的资产时，边界是一个取决于一个价格和时间的表面。推导出估值公式和相关的积分方程。进行了数值实验。