Subject 109 April 2003 question 8 - delta confusion!

[Molly]

Hi all,

I am just watching the online classroom solution to this question. I am a little confused at the derivation of the upstep probability q.
On page 45 of the tables I can see the formula q=exp(r \deltat -d)/(u-d)

It seems the solutions has taken \delta_t to be 1/365. Why is this? I guess I am mainly confused about how to find the \delta of something when it’s not simply \delta on its own. I have written down the results that \delta_s=1 and \delta_c=0 but I don’t necessarily understand the process of finding these.

Please could someone help?

Thanks!
Molly

 

[John Potter]

Molly,

Make sure that the time period (delta) corresponds with the period of the interest rate.
If your interest rate is per annum, you need to put in the change in time in years,

So, let's say that each step in our binomial model is one week and we're told that r = 4% pa, we would need to use exp(0.04/52) because the change in time in years is 1/52

John

 

[Molly]

Molly,

Make sure that the time period (delta) corresponds with the period of the interest rate.
If your interest rate is per annum, you need to put in the change in time in years,

So, let's say that each step in our binomial model is one week and we're told that r = 4% pa, we would need to use exp(0.04/52) because the change in time in years is 1/52

John

Hi John,

Ah that makes a lot of sense. Thank you !

Thanks,
Molly