| Abstract: | Immunization is defined as obtaining a realized yield over a planning period which is greater than, or equal to the promised yield to maturity. Researches in the field of bond portfolio immunization for the last ten years suggest that the duration-based-immunization models are useful in practice due to its simplicity and cost efficiency. However, it has been criticized because of several inherent defects. There have been several other attempts to formulate a bond pricing model which may be interpreted as an indirect approach to the issue for bond immunization management. However, these models are also subject to the similar criticisms made in the duration analysis. In this dissertation, we relaxed the assumptions made in duration theory and postulated a three state variable model of bond pricing in the context of immunization in equilibrium and further extended to include an n state variable model of immunization. Based on modern theories of the term structure of interest rates, the value of a default-free bond of any given maturity can be represented as a deterministic function of n state variables, each of which is assumed to follow a continuous stochastic diffusion process. Using arbitrage arguments, immunization can be shown to require a single partial equilibrium condition on bond prices, which implies, in equilibrium, a partial differential equation should be satisfied by the values of all bonds in the portfolio. Once we derive the stochastic bond price formula, it is possible for investors to be immunized from interest rate risk by the zero risk condition and the no arbitrage condition in the model, with the information on the parameters of the stochastic process for the state variables as well as on the estimates of the risk premium for each state variable. If we select, therefore, the portfolio of bonds for immunization which satisfies the simultaneous equation system, then the value of the asset portfolio at each instance will be precisely equal to that of the liabilities. That is, under the assumptions of continuous trading, an explicit diffusion process and efficient markets, perfect immunization is possible. |
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