基于三因素过程的利率连动息票研究

Pricing and hedging range accrual notes in an affine model with stochastic mean,stochastic volatility,and jumps

本文结合了仿射利率期限结构模型,首次把包含了随机均值、随机波动和跳跃的三因素利率模型应用于利率连动息票的定价和风险对冲过程.给出了利率连动息票(包括固定利率连动息票和浮动利率连动息票)的价值和对冲策略的解析式.数值结果表明,利率连动息票的价值和对冲策略受到以上三个因素的显著影响.其中,代表期望通胀率和市场均衡利率缓慢移动效应的随机均值因素在定价和对冲中扮演着主要的角色.研究表明,利用仿射利率期限结构模型为利率连动息票进行定价和对冲时,忽视以上三个因素将使模型结果产生误差.因此,本文的模型及定价公式为利率连动息票定价和对冲提供了一个更具弹性和一致性的理论框架.

This paper proposes analytic valuation formula of fixed range accrual notes (FiRAN) and floating range accrual notes (FlRAN) in an affine term-structure model incorporating stochastic long-run mean, stochastic volatility, and jumps. Analytic pricing and hedging solutions for range accrual notes are given and these solutions are demonstrated in sensitivity analyses. Our numerical results show all these three factors significantly affect the values and hedging strategies of range accrual notes. Particularly, stochastic mean that represents a composite effect of the expected inflation and a slow evolution in the equilibrium real interest rate plays the most important role in either valuation or hedging. This study suggests that the ignorance of these three factors in term-structure model will result in significant pricing and hedging errors in range accrual notes (RAN). In sum, this study provides a flexible and easily implementable solution in valuing RAN.