Stochastic Interest Rate Models

[Stephen King]

I'm struggling to understand when to use which formula's, in particular when I should be using E(i) or E(1+i), and I keep using the wrong notation in past paper questions.

Has anyone any hints or tips for approaching past paper questions on this topic and how best to determine whether it is a varying or fixed model? All help would be greatly appreciated.

 

[Bharti Singla]

E(i) is the mean rate of interest whereas E(1+i) is the mean of lognormal dist. when (1+i) follows lognormal distribution.
And about fixed and varying rate model, it is given in the qus. whether its fixed or varying like- most of the times, it is mentioned that the rate of interest in any year is independent of any other years→ this means there is a Varying interest rate model. And if the rates of interest is constant over years, means it is fixed rate model.

But I can better help you if you share the qus. which you are stuck in.

 

[Bharti Singla]

Ok, lets see this one.
April 2015, qus.12 (IFOA)

See the first line, it is mentioned the rates are independent, I have highlighted. So, we will proceed accordingly.
Now, see the info given below part(i),
(1+i)~LogN(u,sigma²).
But see carefully 0.04 is given the mean rate of interest i.e.E(i) and 0.12 is the standard deviation of rate of interest i.e.sd(i).
Now, we need to find parameters mu and sigma² in part(ii),(a). And for that, we need mean and var. of lognormal dist. that is

E(1+i)= 1+E(i)= 1.04 and
Var(1+i)= Var(i)= 0.12²

Hope this helps.

 

[Stephen King]

Sorry for the late reply. This was very helpful- Thank you.