- CFA Exams
- 2025 Level II
- Topic 6. Fixed Income
- Learning Module 27. The Arbitrage-Free Valuation Framework
- Subject 4. Pathwise Valuation
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Subject 4. Pathwise Valuation PDF Download
For a n-period binomial tree, there are 2(n-1) possible paths.
For a particular bond, select an interest rate path and the cash flows that are assigned to the path. The cash flow along the interest rate path can then be discounted. The resulting present value is called the pathwise value of that particular interest rate scenario of the bond.
The average of the pathwise values of all the interest rate paths of a bond is the arbitrage-free bond value.
Pathwise valuation produces the same result as backward induction, but it is more readily adaptable for path-dependent securities such as mortgages.
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