Interest Rate Risk Hedging Under The Heath-jarrow-morton Framework

Interest rate risk is the main risk which the fixed income securities investmentmust to face. The development of the financial market and liberalization make themarket interest rates fluctuate drastically. So the management of the interest rate riskhas become a most important question. At the same time, along with graduallyincreased understanding about the characteristic of the interest term structure,academia and practical circle have all become to discuss about the management of theinterest rate risk based on the static and dynamic term structure of interest rate.Based on the study of traditional duration and convexity models and stochasticduration and convexity models, this paper investigated on four specific aspects: thetheory of the interest rate risk measurement, the accuracy of the measurement, thechoice of the immunizing tools and the reasonability of the immunization strategies ofinterest rate risk.First, the multiple-factor stochastic duration and convexity models are established,which based on the HJM models. Five stochastic duration and convexity’scomputable formulas are obtained basing on the five HJM models.Second, introducing the estimate results using nonparametric method, the valuesof the volatility function, which is needed in the stochastic duration and convexitymodels, can be obtained directly. This method can eliminate the influence ofspecification error, simplify the estimate process, and measure improve the accuracy.Third, a method how to choose the immunizing tools is proposed. Two questionsare taken into account. One is the influence of the different choices about theimmunizing tools. The other is the correlation relationship between the differentaccuracy in measuring the interest rate risk of different immunizing tools and theaccuracy of volatility function’s values. An approach to replicate the different fixedincome securities with a simple portfolio which contains three spanning bonds areused. Then choosing the corresponding maturity which has the smallest fluctuation ofthe volatility function’s estimate values as the best maturity which has best estimateof volatility function’s values. The spanning bond corresponded the best maturity is considered to be the best spanning bond. At last, the fixed income securities whosebest spanning bond has the maximum weight are selected.Fourth, based on an analysis of the traditional duration-matched strategy, anacademic shortcoming of this strategy is pointed out. An immunization strategy basedon the optimization methods is deduced from the HJM framework. This strategymakes full use of the theoretic assumptions to the term structure of interest rates andthe definition of interest rate risk under the HJM framework. In addition, the relevantproblems with this strategy are also studied. There are several problems about themultiple interest rate risk factors, high order interest rate risk, and short-sellingconstraints and so on. The empirical results show that by using this strategy theimmunization effects which based on the HJM models’ stochastic interest rate riskmeasures can be improved to a certain degree.Finally, three empirical tests are designed to examine the immunization effect,which based on the stochastic interest rate risk measures under HJM framework, fromdifferent angles. There are several main ideas which are considered in the empiricaltest, such as the different immunization effects between the single-factor andmultiple-factor stochastic interest rate risk measures, between the traditional andstochastic interest rate risk measures, between the parametric and non-parametricstochastic interest rate risk measures, The effects of different rebalancing period andthe different immunization strategies on the immunization effects.