# Fixed Income- Pathwise valuation

How to calculate the number of independent paths in a path-wise valuation method?

Schweser notes say 2^{(n-1)}, n being the number of periods.

However, at a number of places I don’t get the right answer using this formula? Help please!

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It’s

~~2~~^{n}2^{n}.^{−1}With 1 period, there’s 2^{1−1}=2^{0}= 1 path (i.e., discount at today’s spot rate).With

~~1~~period2, there ares22^{2−1}=^{1}= 2 paths:With

~~2~~periods, there are322^{3−1}=^{2}= 4 paths:With

~~3~~periods, there are422^{4−1}=^{3}= 8 paths:And so on.

A 30-year, monthly binomial tree (for valuing a 30-year, monthly-pay mortgage) will have

paths, or slightly more than2^{360−1}= 2^{359}~~2,348,542,582,773,830,000,000,000,000,000,000,000,000,000,000,000,000,000,~~000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

.1,174,271,291,386,915,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000,000

I’ll leave it to you to enumerate them all, but I’ll get you started:

~~356~~more ups), up, up355Simplify the complicated side; don't complify the simplicated side.

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this is super helpful….thanks S2000magician…you are a saviour!

My pleasure.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

http://financialexamhelp123.com/

Studying With

i am confused now. in the Practise Problems in CFAI website. under Ahti Maalouf Case Scenario, the four-year bond requires 2

^{3}= 8 paths. Why is is not 2^{4}= 16 pathsThe interest rate in each node represents a one-period forward rate.

For a four-year bond, the final (4th year) cash flow (principal + coupon) will be discounted using the 1-year forward rate in Year 3, which means you only need the interest rate tree up to Year 3 only, hence there is only 2

^{(4-1)}= 8 paths.——————————————

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As you should be, because I was mistaken. I was thinking of a tree for stock prices, not an interest rate tree.

Indeed, for a binomial interest rate tree, it should be 2

^{n−1}. I’ve fixed my earlier post.Simplify the complicated side; don't complify the simplicated side.

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Thanks for your confirmation.!

My pleasure.

Simplify the complicated side; don't complify the simplicated side.

Financial Exam Help 123: The place to get help for the CFA® exams

http://financialexamhelp123.com/