## FRm2-MR 11

anbu.edu
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### FRm2-MR 11

45.2 Assume that change to up-state (u) = + 20 bps and change to down-state (d) = -10 bps
in a recombining binomial interest rate tree where p = 50%. The date 0 rate is 3.0%. What is
the date 12, state 5 interest rate?
a) 3.3%
b) 3.6%
c) 3.9%
d) 4.2%

Date 12 is the final state of the tree and therefore is a binomial distribution with n = 12 (i.e.,
13 final states)
As state 0 is the bottom-most node (following Tuckman), state 5 refers to any sequence
(recombining!) of 7 down jumps and 5 up jumps. Therefore, this node equals (-10 bps * 7) +
(+20 bps * 5) + 3% = 100 bps - 70 bps + 3% = 3.3%

My doubt is how did they conclude 7 down jumps and 5 up jumps.. please help me understand

edupristine
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Posts: 704
Joined: Wed Apr 09, 2014 6:28 am

### FRm2-MR 11

Hi,
A node is referred to as (n, s) where n = 0,1,...... N is the date, and s = 0,1,2...... n denotes
the state, numbered from below.

In the question above, date=12 and state, s = 5. If state is equal to 5, then you will have to traverse the tree up 5 times to reach 5th state, hence up jumps will be 5. To calculate the down jumps, subtract up jumps (i.e 5) from the date i.e 12. So, down jumps = 12-5=7.