Why do future interest rates follow a lognormal distribution ?

[Nabil Janmohamed]

Hi,

I know in CT1 we calculated the stochastic interest rate using a lognormal distribution but in CT4 question 1.3 where of chapter 1 the solutions say that future interest rates will follow a lognormal distribution (see attached). I am curious to know why this is the case?

Best,

Nabil

 

[Dillon]

Hi,

I know in CT1 we calculated the stochastic interest rate using a lognormal distribution but in CT4 question 1.3 where of chapter 1 the solutions say that future interest rates will follow a lognormal distribution (see attached). I am curious to know why this is the case?

Best,

Nabil

That is just given an example of a distribution that may be assumed.

In reality, we don't know what the distribution of future interest rates is going to look like.

The lognormal distribution is a distribution with some nice properties that makes it useful for modelling interest rates (e.g not too complex and ensures non-negative interest rates).

There are many other interest rate models that are used in the real world, you'll come across a few of them in CT8 (although if I remember correctly, most of these are based on the assumption of a lognormal distribution).

 

[Nabil Janmohamed]

Thanks Dillon, this make a lot more sense now.