Introduction

This chapter provides a brief introduction to some basic concepts from interest rate theory and financial mathematics and applies these theories for the calculation of market values of life insurance liabilities. There exists a huge amount of literature on financial mathematics and interest rate theory, and we shall not mention all work of importance within this area. Some basic introductions are Baxter and Rennie (1996) and Hull (2005). Readers interested in more mathematical aspects of these theories are referred to Lamberton and Lapeyre (1996) and Nielsen (1999). Finally we mention Björk (1997, 2004) and Cairns (2004).

The present chapter is organized as follows. Section 3.2 demonstrates how the traditional actuarial principle of equivalence can be modified in order to deal with situations with random changes in the future interest rate, i.e. to the case of stochastic interest rates. This argument, which involves hedging via so-called zero coupon bonds, leads to new insights into the problem of determining the market value for the guaranteed payments on a life insurance contract. Section 3.3 gives a more systematic treatment of topics such as zero coupon bonds, the term structure of interest rates and forward rates. In addition, this section demonstrates how versions of Thiele's differential equation can be derived for the market value of the guaranteed payments.