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Suppose I have a loan where the cash flows and the discount rate are calculated using LIBOR + 100 bps
If I wanted to calculate how much a unit of risk (1 bp) is worth in USD, I understand that I should only shift 1bp in the discounting curve - and NOT in the projected cash flows + discounting curve -, is this correct?
Any insight on this would be appreciated!
Then how much 1 bp would be worth, would be equal to the MTM change= Orig MTM - Shifted MTM.
(Related discussion: IRS - sensitivity to estimation (projection, coupon) curve and discounting curve )
If the loan is HY/distressed/already defaulted, then its price is driven more and more by the recovery assumption, rather than by intrest rate. Some desks that specialize in distressed debt even have models that predict how much the recovery assumption is driven by interest rates. Still, it's a small sensitivity.
Having said this, let us assume that the loan is IG and its mark is driven by the interest rates. You have two curves:
1 the curve used to project the unset coupons, i.e. the swap curve
2 your financing (funding, discounting) curve for this loan.
If these two curves move in parallel, which is the most common behavior in the market, then you have lots of P&L from the "+100 bps" part of your coupons, because this part is only sensitive to the discounting curve - essentially a fixed coupon. But the P&L from the "index" part of your floating coupons will be offset by the P&L from the present value of the principal repayments.
A more comprehensive set of interest rate risk measures might include the sensitivities to the spread between these two curves, and various scenarios other than a 1bp parallel shift, e.g. 2nd and 3nd principal components, larger shocks...
