ABSTRACT
This chapter discusses the survey some new results concerning the term structure of interest rates and discuss actuarial applications. The term structure of interest rates exhibits the relationship among the yields on default free debt instruments of different maturities. The arbitrage principle together with some assumption about investors tastes is invoked to obtain the price of a pure discount bond of arbitrary maturity. The development is completed by invoking assumption to prevent riskless arbitrage by reasoning similar to that used to derive the Black Scholes option pricing formula. Non-zero values can be chosen to correspond to a liquidity premium theory of the term structure. The importance of the maturity structure of the liabilities in selecting appropriate assets has been widely recognized in actuarial circles. To achieve immunization under the stochastic models the mean term of the assets has to be made equal to the mean term of the liabilities as in Redington's theory.
