A consistent relationship between interest rate risk factors and the changes in the value of a financial instrument induced by them is established through the decomposition of the financial instrument into cash flows insofar as such a decomposition is possible. The philosophy behind this approach is that the value of any financial instrument is equal to the sum of all discounted, expected future cash flows. The decomposition into expected future cash flows can, in general, be accomplished to a point where the size of the cash flow no longer depends explicitly on the interest rate (in the case of interest rate options, this only holds when the option price is approximated linearly as a function of the interest rate). The interest rate risk of an instrument then consists solely in the fact that the discount factors used in computing the instrument’s present value at a specified value date change with changes in the interest rates. However, the size of the cash flows can by all means be affected by other risk factors; these could be foreign exchange risk or other price risks influencing the value of the instrument.
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