Term Structure Interest Rates

Hi Jia

Some thoughts below:

1) Best thing to do with these questions on spot rates / forward rates / bond prices is to draw yourself a timeline and mark on what info you have and what you need to know. Then the question turns into a fairly straightforward (CT1-type) discounting exercise.

For example in CT8 April 2015 Q10(i), look at the time line in the attached picture:



To work out (b), which is B(0,1), ie the price at time 0 of a bond that pays 100 at time 1, we discount the cashflows:

B(0,1) = 100 exp(-0.02)

To work out (a), we can use B(0,4), ie the price at time 0 of a bond that pays 100 at time 4 and discount the cashflows:

86.94 = B(0,4) = 100exp(-a)exp(-0.03)exp(-0.04)exp(-0.02)

2) I would say not, no longer on syllabus, however you do need to be aware of the limitations of one-factor models (Core Reading Chapter 18, Pages 27 and 28), and hence it is useful to know that such a thing as two-factor models exist. But no to learning the formula for the two-factor Vasicek.

3) Yes, I would say that you could be expected to deduce the difference / advantage from looking at the H&W SDE compared with the Vasicek SDE. With H&W we see that the mean parameter, mu(t), can vary over time (it is time inhomogeneous). Hence, we have more parameters with H&W: alpha, sigma and multiple mu's, than with Vasicek. This makes H&W better for calibrating to past / current data.

4) The notation in the Core Reading changed from B(0,t) to P(0,t) for the 2019 syllabus. You'd be fine using either in the exam, indeed you may see B or P in exam questions. Both represent the bond price.

I wish you the very best of luck for next week.
Anna