Research On Hedging Of Fixed Income Securities

The fixed income market is an important part of the financial markets. Under thebackground of rapid growth and severe fluctu ation of the fixed income market, it’s ofcritical significance to research on the risk hedging of fixed income securities so as tobuild more accurate immunization models, wh ich can be u seful for the investors andeven the regulators.In this dissertation, a syst ematic and intensive research is m ade on hedging ofinterest rates risk of treasury bonds based on both statistic and dynamic interest ratesterm structure models and on hedging of defaultable bonds based on the factor modelsof credit portfolio.First, based on a concise introduction of risk hedging tools under statistic interestrates term structure m odels, another curv ature factor is introduced to extend theNelson-Siegel duration vector m odel to the Svensson duration vector model and theFour-Shape-Factor duration vector m odel. Empirical te sts base d on the data ofShanghai Security Exchange (hereafter SSE) show that although the second curvaturefactor explains little part of the variance of interest rates term structure, interest ratesrisk hedging errors can be reduced sign ificantly by introduci ng it. Besides, theFour-Shape-Factor duration vector model has less param eter to be estim ated andperforms better than the Svensson duration vector model, which m akes it the b ettermodel for interest rates risk hedging.Second, after a brief introduc tion of dynamic Nelson-Siegel-style models whichare proved to be effective in interest rates term structure forecasting, another curvaturefactor is introduced to extend the dynamic Nelson-Siegel-style models to the dynamicFour-Shape-Factor-style models. Besides, bo th of these two cla sses of models aremodified by m odeling their first-dif ferenced parameter series. Em pirical tests basedon the data of SSE show that the incorpor ation of the seco nd curvature factor canimprove the performance of interest rates term structure forecasting significantly andthe firs t-differenced modification of thes e tw o class es o f m odels can also y ieldsmaller and more stable forecasting errors.On the basis of forecasting of interest rates term structure, bonds’ prices ar eforecasted by discounting their future cash flows, which are introd uced to theFour-Shape-Factor duration vector model. Empirical tests based on the SSE data show that the in corporation of the f orecasting inf ormation about the inte rest rates ter mstructure can im prove the interest ra tes risk hedging perform ance of theFour-Shape-Factor duration vector model significantly.Third, based on a system atic introduction of t he stochastic duration under thedynamic interest rates term structure m odels, the stochastic duration vector of theAffine T erm S tructure Model is derive d, whereas the stochastic duration underVasicek&CIR Model is in terpreted as the degra dation in the f orm ofone-dimensional stochastic duration vector. Empirical tests ba sed on the SSE datashow that the four-factor stochastic duration vector performs significantly better thanstochastic duration when hedging the intere st rate risk of treasure bonds. Besides,stochastic duration vector of the four-factor Non-Gaussian Af fine Term S tructureModel yields sm aller hedging errors than th at of four-factor Gaussian Af fine TermStructure Model.Besides, the interest rates risk hedgi ng errors under both the statistic interestrates term structure m odels and dynam ic in terest rates term structure m odels arecompared. It shows that Four-Shape-Factor duration vector model with the forecastinginformation of the intere st rates term structure incorporated performs best, whereasthe stochastic duration vector of the four-factor Non-Gaussian Affine Term StructureModel perf orms even worse than the F our-Shape-Factor duration vector m odelwithout the forecasting information of the interest rates term structure incorporated.Finally, based on a laconic introduction of the default contagion m odel and thefactor models of credit portf olio, default contagion effect is introduced to the factormodels of credit portfolio, under w hich the analytical results for hedging the creditrisk of portfolio with linear combinations of systematic risk factors and for Hoeffdingdecomposition of the portfolio systematic loss into a sum terms depending on the riskfactors are presented. For hom ogenous cr edit portfolio, the expectation of itssystematic loss as well as the position of the risk-free bond in the hedging portfolioincreases after th e default contagion effect is in troduced. Besides, when the d efaultprobability of the counterparty in the homogenous portfolio is relatively low (h igh),the position in the systematic risk factors increases (decreases) after the incorporationof default contagion ef fect. Simulation results under the two system atic risk factorscondition show that when the confidence level increases, the CVaR of systematic lossincreases too, which is m ainly attributed to not the expectation term but the factorco-movements term. Besides, if the fraction o f default in creases, which m eans the default contagion ef fect strengthens, the CV aR of systematic loss increases, whichmainly results from the factor co-movements term too.