Closed Form Solutions for Term Structure Derivatives with Log‐Normal Interest Rates
推导出一个统一模型，为利率上限/下限和零息债券期权提供闭式解，关键假设是匹配合约期限的简单利率服从对数正态分布，且该假设与Heath-Jarrow-Morton模型在特定波动率下一致。
ABSTRACT We derive a unified model that gives closed form solutions for caps and floors written on interest rates as well as puts and calls written on zero‐coupon bonds. The crucial assumption is that simple interest rates over a fixed finite period that matches the contract, which we want to price, are log‐normally distributed. Moreover, this assumption is shown to be consistent with the Heath‐Jarrow‐Morton model for a specific choice of volatility.