具有相关波动因子的广义随机波动HJM模型  

Generalized Heath-Jarrow-Morton model with stochastic volatility and correlated factors

作　　者：杨宝臣[1] 苏云鹏[1] 

机构地区：[1]天津大学管理与经济学部,天津300072

出　　处：《管理科学学报》2011年第9期77-85,共9页Journal of Management Sciences in China

基　　金：国家自然科学基金资助项目(70771075);教育部博士点基金资助项目(200800560032);教育部新世纪优秀人才支持计划资助项目(NCET-08-0397);长江学者和创新团队发展计划资助项目(IRT1028);天津大学自主创新基金资助项目

摘　　要：基于Heath-Jarrow-Morton(HJM)模型框架,将远期利率波动率设定为服从广义均值回归平方根过程的随机变量,以刻画隐性随机波动因子的动态特性,并通过将漂移项限制条件推广至波动因子之间,以及利率波动率的变化与利率变动之间存在相关性情况,建立了广义的多因子HJM模型.在该模型框架下,基于一类特定波动率设定形式将风险中性概率测度下的收益率曲线表示为服从仿射扩散过程的有限维状态向量的函数形式,并推导出零息债券的准解析定价公式.并且,基于市场风险价格的广义仿射设定形式,将以上结果推广至现实概率测度下.Heath-Jarrow-Morton model is generalized by extending the no-arbitrage drift restriction with nonzero instantaneous correlations between volatility factors and setting forward rate volatilities subject to generalized mean-reverting square-root processes and correlated with innovations to forward rates.In the framework above,the dynamics of the term structure under the risk-neutral probability measure are described in terms of a finite number of state variables that jointly follow an affine diffusion process under a certain volatility specification,and a quasi-analytical formula for zero coupon bond prices is derived based on transform techniques.Then the result is further generalized to the case under the actual probability measure through the extended affine market price of risk specification.

关 键 词：HJM模型 随机波动率 相关性 马尔科夫转换 仿射实现 

分 类 号：F830.91[经济管理—金融学]