Stochastic Interest Rate

In Chaps. 1 to 5, it is assumed that the rate of interest in the calculations of actuarial present values is deterministic and usually constant over the period of policy. However, the assumption of deterministic interest will be rarely realized in practice, particularly for long-term policies. Chapter 6 introduces, in brief, stochastic models for interest rates and calculation of premiums for some products in this setup. In this chapter we discuss how the randomness in the interest rates is captured and how it affects the actuarial present values of cash flows. Section 6.2 discusses how different scenarios of time-varying interest rate are modeled by a random variable and how premiums can be computed under this setup. Section 6.3 discusses how to obtain the actuarial present values of cash flows if the interest rates for the period under study are assumed to be independent and identically distributed random variables. The particular case of lognormal distribution is investigated in detail. In Sect. 6.4, the assumption of independence is relaxed, and interest rates over the time period are modeled by an appropriate time series model. MA(1) model for the interest rates is studied in detail. These methods are illustrated with the corresponding R code.