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maxh1994
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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.
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1420787
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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?
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ghostwalker
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(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 E(X)=\sum x_iP(X=x_i)

where x_i 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.
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1420787
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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.
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maxh1994
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(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 E(X)=\sum x_iP(X=x_i)

where x_i 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?
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ghostwalker
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(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.
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maxh1994
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(Original post by ghostwalker)
Yep.
Thanks man, got it.
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