FM for Actuaries

316 CHAPTER 10
The empirical means and variances are as follows:
Figure 10.1: Histograms of simulated results in Example 10.4
(a) a(10) (b)
1
a(10)
(c) a 10⌉
(d) ä 10⌉
(e) s 10⌉
(f) ¨s 10⌉
a(10)
1
a(10)
a 10⌉ ä 10⌉ s 10⌉ ¨s 10⌉
Mean 2.1656 0.4836 6.8382 7.3546 14.5018 15.6674
Variance 0.2224 0.0110 0.5678 0.4383 3.5101 5.3524
10.5 Dynamic Term Structure Model
Each yield curve shown in Figure 3.4 is for a particular date. If we examine the
yield curve on another date, the shape of the curve may be different. Figures 7.3
and 7.4 plot the UK and US yield curves in the period January 2002 to December
2015, respectively.
In Section 7.7 we discuss some static term structure models which explain the
shape of the spot-rate curve (i.e., the term structure of interest rates) at a fixed date.
In the literature there are some advanced models that can characterize the shape
of the term structure as well as its evolution simultaneously. In other words, these
approaches try to model the dynamics of the observed yield curves (i.e., the whole
surface area of yield curves as in Figure 7.3 or Figure 7.4).