Level-Dependent Annuities: Defaults of Multiple Degrees
研究了当公司财务困境导致债务利息支付停止或减少时，如何对层级依赖型年金合同进行估值，其中年金率取决于基础资产价值，并给出了几何布朗运动假设下的闭式解公式，适用于美国破产法第11章下的公司债务和层级依赖利率贷款估值。
Abstract Motivated by the effect on valuation of stopped or reduced debt coupon payments from a company in financial distress, we value a level-dependent annuity contract where the annuity rate depends on the value of an underlying asset process. The range of possible values of this asset is divided into a finite number of regions, with constant annuity rates within each region. We present closed-form formulas for the market value of level-dependent annuities contracts when the market value of the underlying asset is assumed to follow a geometric Brownian motion. Such annuities occur naturally in models of debt with credit risk in financial economics. Our results are applied for valuing both corporate debt with suspended interest payments under the U.S. Chapter 11 provisions and loans with contractual level-dependent interest rates.