【作者】 陈翔；

【导师】 叶中行；

【作者基本信息】 上海交通大学 ， 概率论与数理统计， 2010， 硕士

【摘要】 主成分分析是一种有效的根据利率期限结构的历史数据来得到影响其变动的主要因子或方向的方法,这样我们就可以将传统的只对假定利率期限结构发生平移变化的单方向免疫策略扩展到由主成分因子的各种线性组合导致的变化下的多方向免疫策略。而且主成分带来的维数简化使得我们可以利用低差异序列来进行拟蒙特卡洛模拟,得到尾部分布性质更好的组合损失分布,在此基础上得到更有效的VaR(在险价值)与Expected Shortfall(期望损失值)的值,并且所花的时间比传统的蒙特卡洛方法要短。本文首先讨论怎样选取合适的利率期限结构模型来拟合银行间固定利率国债市场的利率期限结构,并加以实证。然后对曲线上关键期限点利率变动的历史数据序列应用主成分分析方法来进行分析,得到影响利率期限结构变动的主要因子。进而介绍债券组合的传统的单方向免疫策略,在此基础上尝试构建基于主成分的多方向免疫策略,假定一个负债项的固定现金流的国债组合,得到在利率期限结构的各种平移或非平移变化下的免疫组合。最后利用所得到的主成分来大大简化风险因子的个数,从而应用基于低差异序列的拟蒙特卡洛方法来得到债券组合的损失分布和其在险价值(VaR)与期望损失值(ExpectedShortfall)的值。更多还原

【Abstract】 Principal Component Analysis is proved to be an effective method of using thehistorical spot interest rates changed data to determine the best single direction and thebest set of fundamental directions in which to anticipate spot rate changes. Under thisbase,we can develop the multi-direction immunization model that allow the term struc-ture to shift in directions that are the linear combination of the first three main compo-nents we choose,beyond the traditional single direction immunization strategy,whichis valid only if term structure shifts are parallel.And another advantage is that withthe reduced dimensions of risk factors,usually we use the first three principal compo-nents to represent the change of the term structure.The Quasi Monte Carlo Simulation,based on deterministic and low discrepancy sequence,will do much better to get theloss distribution,especially on the tails,and get more effective estimates on the valueof VaR and Expected shortfall.The first part of this paper is to choose the proper interest rate model to constructthe spot yield curve on the fixed-rate national debts chose from the domestic inter bankbond market,then we apply the Principal Component Analysis on the historical spotrates changed data corresponding to the key rate set for the curve.Then we will discussthe traditional single direction and set up multi-direction(represented by the principalcomponents) immunization model on bond portfolio,and get the hedge portfolio usedfor immunization on the supposed fixed income portfolio under each types of the termstructure shifts.At the last step,We will use the Qusai Monte Carlo Simulation to getthe loss distribution and estimates on the value of VaR and Expected shortfall.更多还原