Credit Risk and Collateral Effects in Multiple-Curve Rates
Summary
The document explains why interest-rate indices with different tenors can have different values and why derivatives referencing them may require separate curves. It attributes part of the spread between six-month and three-month LIBOR to the additional bank credit exposure associated with the longer lending period. A basis swap exchanging the two indices plus a spread illustrates how markets express that difference; modeling the tenor spread may require credit techniques.
It also explains that one-year LIBOR can exceed a one-year swap rate because the swap is described as a sequence of shorter three-month LIBOR periods, with less credit exposure in the underlying index. This is distinct from credit risk on the swap itself, which the answer treats as negligible. The response attributes long-term swap rates below Treasury yields mainly to regulation and the balance-sheet cost of holding assets such as Treasuries. These are concise explanations rather than a comprehensive theoretical framework, and the document does not quantify the effects or discuss calibration in detail.
Key ideas
- Different LIBOR tenors can reflect different levels of bank credit risk over the lending period.
- Basis swaps exchange tenor indices and their spread can represent the difference between those rates.
- Credit modeling can be used to describe the term structure of tenor spreads.
- A one-year swap rate based on shorter LIBOR periods may be below one-year LIBOR because of lower underlying index credit exposure.
- Regulatory balance-sheet costs can help explain why long-term swap rates trade below Treasury yields.
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# LMM & multiple curves # LMM & multiple curves I was reading through a paper that attempted to present a theoretical explanation for the divergence in value of different LIBOR tenors (and thus for the use of different curves for different tenors). The author's framework explained differences in terms of FRA and basis swap spreads (in Conjecture 6, p.19), and I was wondering: - have any comprehensive theoretical frameworks been developed that are used in practice? - are there any other reasons (beyond empirical fitting) for using multiple curves (inspired by the answers to this question)? Finally, in the framework of multiple curves, is it then appropriate to say that 1Y LIBOR is above 1Y swaps because the swaps use OIS discounting (and are collateralized)? If so, does this extend to explaining any of the difference in long term rates (10Y swaps below 10Y treasuries), or are these dynamics better explained by regulatory environments and repo markets? Thanks ## Answer by dm63 (score 2) https://quant.stackexchange.com/a/28354 As an example: 6 month libor is typically higher than 3 month libor because of the extra credit risk in lending to banks for an additional 3 months. Derivatives on 6 month libor have to take this into account. For example, a 5yr basis swap exists where 6 month libor can be swapped for 3 month libor plus a spread. Credit modeling techniques would need to be applied to model the term structure of this spread, and other tenor spreads. In your example, 1 year libor is higher than the 1 year swap rate because the latter is equivalent to a chain of four 3 month Libors, so has less credit risk. Note that we are talking about the credit risk of the underlying rate index, not of the swap itself which is negligible. 10 year swaps being below 10 year Treasuries is mostly explained by the current regulatory environment, as you suggest. Specifically, the cost of holding assets such as Treasuries on balance sheet.
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