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# Maths/Finance watch

1. Doing a financial elective which I am really struggling with. Think this has got something to do with trinomial interest rate models?
Any help will be really appreciated

Time is counted from the present t = 0 in years. Suppose for the first 12 years the force of interest is 5%. After that it changes to 3% with probability 0.25, remains unchanged with probability 0.5 and increases to 7% with probability 0.25.

Find the expected present value of a continuous payment stream of £143 per annum for 20 years, beginning at time 0.
2. I would do it using recurrence relations, but that's still a fairly labour intensive method of getting to the answer. Would be interested in hearing a better method!

I'm guessing that calculating an expected interest rate after 12 years will be needed to express the present value as a single function?
3. (Original post by maxh1994)
Doing a financial elective which I am really struggling with. Think this has got something to do with trinomial interest rate models?
Any help will be really appreciated

Time is counted from the present t = 0 in years. Suppose for the first 12 years the force of interest is 5%. After that it changes to 3% with probability 0.25, remains unchanged with probability 0.5 and increases to 7% with probability 0.25.

Find the expected present value of a continuous payment stream of £143 per annum for 20 years, beginning at time 0.
I presume working out the value for a fixed interest rate over a period of time is straight forward for you.

So, assume it changes to 3% after 12 years, and work out the value.

Assume it remains at 5% and work out the value.

Etc.

Then

where ranges over the three values.

No trinomials required.

I am presuming that once the interest rate changes after 12 years, it then remains fixed at that new value.
4. Is the implication of finding the "expected present value" not looking for an expression that can be evaluated to give an answer for any given value 't'?

If not and just a final answer is being sought, then recurrence relations and the usual method for expected values would be my choice.
5. (Original post by ghostwalker)
I presume working out the value for a fixed interest rate over a period of time is straight forward for you.

So, assume it changes to 3% after 12 years, and work out the value.

Assume it remains at 5% and work out the value.

Etc.

Then

where ranges over the three values.

No trinomials required.

I am presuming that once the interest rate changes after 12 years, it then remains fixed at that new value.
So once i have worked out the values at 3%,5%, 7%, I then times them by their probabilities and add them all together?
6. (Original post by maxh1994)
So once i have worked out the values at 3%,5%, 7%, I then times them by their probabilities and add them all together?
Yep.
7. (Original post by ghostwalker)
Yep.
Thanks man, got it.

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