In this paper, the fair price of an American-style resettable convertible bond (CB) under the Black–Scholes model with a particular reset clause is calculated. This is a challenging problem because an unknown optimal conversion price needs to be determined together with the bond price. There is also an additional complexity that the value of the conversion ratio will change when the underlying price touches the reset price. Because of the additional reset clause, the bond price is not always a monotonically increasing function with the underlying price, which is impossible for other types of the CBs. Of course, the problem can be dealt with using the Monte-Carlo simulation. But, a partial differential equation (PDE)/integral equation approach is far superior in terms of computational efficiency. Fortunately, after establishing the PDE system governing the bond price, we are able to present an integral equation representation by applying the incomplete Fourier transform on the PDE system.

中文翻译：

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使用积分方程法对可重置可转换债券定价

在本文中，计算了带有特定重置条款的Black-Scholes模型下的美式可重置可转换债券（CB）的公允价格。这是一个具有挑战性的问题，因为需要与债券价格一起确定未知的最佳转换价格。还有一个额外的复杂性，即当基础价格触及重置价格时，转换比率的值将发生变化。由于增加了重置条款，债券价格并不总是随基础价格单调增加，而其他类型的可转债则不可能。当然，可以使用蒙特卡洛模拟解决该问题。但是，偏微分方程（PDE）/积分方程方法在计算效率方面要好得多。幸好，