Principal Component Analysis And Quasi Monte Carlo Simulation On Debt Portfolio Management

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.