Where interest rate risk in the banking book comes from · RiskAtoms Academy

By the end you will be able to

1Name the four sources of interest rate risk in the banking book: repricing (gap), yield curve, basis and option risk.
2Find repricing and basis risk on a bank's balance sheet and size them.
3Explain why the shape of a rate move matters as much as its size.
4Explain why customer options, such as prepayment, cost the bank whichever way rates move.

Why it matters

In 1980 the US savings and loan industry, lenders that held fixed-rate home loans and paid short-term rates on deposits, made $781 million. In 1981, after interest rates soared, it lost $4.6 billion, with almost no bad loans (FDIC). The loans were sound. The rates on them were not changing, while the rates on the deposits funding them were. That is the oldest source of interest rate risk in a bank, and there are three more.

Core explanation

Four ways a rate move reaches a bank

Illustrative dataRiskAtoms Bank plc's banking book

The same £67bn balance sheet as Module 3.5, on one made-up reporting date, in pounds, now with how each line reprices: fixed, floating or administered, its customer rate, a SONIA curve with Bank Rate at 4.00%, a macro hedge and a structural hedge. The figures are round illustrative values, not any bank's data. Every lesson in Module 3.6 uses this book, so the figures agree.

This lesson relies on: shocks added in full to customer renewal rates; floating items repricing at their next reset; deposit rates moving by their betas a month after the market; and SONIA moving with Bank Rate unless a basis move is set.

L3.6.01: What ALM does introduced the book and its two lenses. Here we ask where the exposure comes from. The Basel Committee's 2004 principles listed four sources: repricing, yield curve, basis and option risk. The 2016 standard regroups them into three, putting the first two together as gap risk, "parallel risk" and "non-parallel risk" (SRP31.2). Each one shows up on RiskAtoms Bank's book.

1. Repricing (gap) risk: when the rates change

Repricing risk comes from assets and liabilities resetting their rates at different times. The Basel 2004 example is a long fixed-rate loan funded by a short deposit: if rates rise, the deposit costs more at once while the loan earns the same. RiskAtoms Bank is the other way round: its funding is mostly current and savings accounts that move little, while £19.0bn of reserves, trackers and corporate loans float. So a rise helps NII: +£91.7m in the first year for +100bp, and −£94.8m for −100bp. Who gains and who pays:

Repricing risk also has a value side. The five-year fixes, £15.0bn at 3.8%, would be written today at 4.99%: their cash flows are fixed, so every rise in rates lowers their present value. On the whole book, EVE falls by £98.0m for +100bp. L3.6.03: Repricing gap analysis measures repricing risk with the gap.

2. Yield curve risk: how the curve changes shape

Rates rarely move in parallel. Yield curve risk is the risk from the curve steepening, flattening or twisting (L1.3.08: The yield curve: spot and forward rates), and it bites even when a bank is hedged against parallel moves (Basel 2004, paragraph 14). Compare two of the standard shocks:

SONIA zero rates, today and after two shocks
Tenor	Today	Parallel up	Steepener
Overnight	3.92%	6.67%	1.16%
1 years	4.01%	6.76%	2.36%
2 years	4.08%	6.83%	3.29%
3 years	4.13%	6.88%	4.02%
5 years	4.21%	6.96%	5.02%
7 years	4.25%	7.00%	5.63%
10 years	4.29%	7.04%	6.13%

Both push ten-year rates up. But the steepener cuts the overnight rate by 276bp, and next year's NII lives at the short end: year-1 NII rises £254.7m in parallel up but falls £191.6m in the steepener. The bank's exposure depends on the shape, not just the size.

The six standard shocks on the book, £m
Shock	ΔNII, year 1	ΔEVE
Parallel up	+£254.7m	−£257.2m
Parallel down	−£263.3m	+£251.7m
Steepener (short down, long up)	−£191.6m	−£79.6m
Flattener (short up, long down)	+£253.7m	+£10.2m
Short rates up	+£337.5m	−£119.4m
Short rates down	−£307.4m	+£99.8m

3. Basis risk: when two indices part

Basis risk arises when positions reprice at the same time but off different indices. RiskAtoms Bank's reserves, trackers and deposit rates key off Bank Rate. Its floating corporate loans and the floating legs of its swaps key off SONIA, which normally fixes a few basis points under Bank Rate but need not stay there. Net, the bank receives SONIA on £13.2bn: £10.0bn of corporate loans plus £19.2bn on the macro hedge, less £16.0bn paid on the structural hedge. If SONIA slipped 25bp below Bank Rate, NII would fall by £28.9m a year, with no change in Bank Rate at all. L3.6.07: Basis risk goes further.

4. Option risk: when customers choose

Option risk comes from choices built into products. The Basel standard splits it into automatic options, such as caps and floors, and behavioural options, exercised by customers for reasons that include, but are not only, rates (SRP31.2). The book has three:

The options in RiskAtoms Bank's book

What makes option risk different is its asymmetry. Prepayment costs NII in both directions: −£2.86m in the first year of parallel down (old high fixes leave and are replaced cheaply) and −£5.73m in parallel up (old cheap fixes stay longer instead of renewing at higher rates). Small in one year, larger in value, and always against the bank: it is short the option.

Sort itName the source

Which source of interest rate risk does each case show?

A building society funds five-year fixed mortgages with one-year fixed-rate savings bonds.
A bank hedged against parallel moves loses when two-year rates rise and ten-year rates fall.
Corporate loans reset to three-month SONIA while savings rates follow Bank Rate; SONIA falls 30bp further than Bank Rate.
Borrowers on fixed rates refinance in a wave after a big rate cut.
A corporate loan's rate is capped at 7%, and SONIA goes to 8%.

The formal version

The year-1 change in NII is the sum of each position's change, with $s_i$ = +1 for what the bank earns and −1 for what it pays. On the book, for +100bp:

\begin{aligned} \Delta\text{NII} &= \sum_i s_i\,\Delta(\text{interest}_i) \\ &= \text{£}302.8\text{m} - \text{£}108.6\text{m} - \text{£}110.4\text{m} + \text{£}131.9\text{m} - \text{£}124.0\text{m} \\ &= \text{£}91.7\text{m} \end{aligned}

Basis. A net position $P$ on one index, a basis move $\Delta b$ and an average wait $\bar t$ until the next reset give

\begin{aligned} \Delta\text{NII}_{\text{basis}} &= P \times \Delta b \times (1 - \bar t) \\ &= \text{£}13.2\text{bn} \times (-0.25\%) \times \left(1 - \tfrac{1.5}{12}\right) = -\text{£}28.875\text{m} \end{aligned}

The SONIA positions reset quarterly in three monthly batches, so the first reset is 1.5 months away on average. The formula matches the full model exactly here, because nothing else moves.

Options. A position with an option is not linear in the rate move: its change for $+\Delta r$ is not minus its change for $-\Delta r$ . For the prepayment option on the book, both are negative:

\Delta\text{NII}_{\text{prepay}}(+275\text{bp}) = -\text{£}5.73\text{m}, \qquad \Delta\text{NII}_{\text{prepay}}(-275\text{bp}) = -\text{£}2.86\text{m}

Try it

Pick a shape for the rate move, add a basis move between SONIA and Bank Rate, and switch the prepayment response on or off. The year-1 NII change splits into its sources. Try parallel up against the steepener first, then add a basis move of −25bp.

Try itMove the curve

Shape of the rate move (Basel standard shock, sterling sizes)

SONIA against Bank Rate (basis)together

Mortgage prepayment

SONIA zero curve todayAfter the steepener shock

ΔNII, year 1−£191.6m

ΔEVE−£79.6m

… from the curve move (gap and curve risk)−£189.7m

… from basis£0.0m

… from prepayment (option risk)−£1.9m

Prepayment's part of ΔEVE−£6.4m

Illustrative book. Bank Rate and SONIA start at 4.00%; the post-shock floor is 0%. The basis move shifts SONIA against Bank Rate from each SONIA reset onwards; it does not change EVE here, which discounts on one curve.

Worked example

Sizing basis risk on the book

ALCO asks: if SONIA fixed 25bp below Bank Rate for a year, what would it cost? Everything else stays where it is.

From positions to a number

Step 1 of 4

1
Find the SONIA positions
$\begin{aligned} \text{Corporate loans (receive SONIA)} &= \text{£}10.0\text{bn} \\ \text{Macro hedge (receive SONIA)} &= \text{£}19.2\text{bn} \\ \text{Structural hedge (pay SONIA)} &= -\text{£}16.0\text{bn} \\ P &= \text{£}13.2\text{bn} \end{aligned}$

Regulatory lens

The Basel IRRBB standard (SRP31.2) defines gap risk, basis risk and option risk, and expects banks to measure each, with gap risk covering both parallel and non-parallel moves. Its six standard shocks (L3.6.06: The standard shock scenarios) test parallel and non-parallel moves; banks add their own basis and option scenarios. The supervisory detail is in M4.5: Liquidity and IRRBB regulation, and the prepayment and deposit models that drive option risk are in M6.7: Liquidity, ALM and behavioural models.

Spark Atoms

Spark AtomInsolvent on paper, with good loans

At the end of 1982, 415 US savings and loans with $220 billion of assets were insolvent on the book value of their tangible net worth. Industry tangible capital had fallen from 5.3% of assets in 1980 to 0.5% in 1982. Credit problems were rare: most assets were fixed-rate home mortgages, and the damage came from the interest rate mismatch (FDIC, History of the Eighties, chapter 4).

Spark AtomFour sources became three

The 2004 Basel principles named four sources of interest rate risk. The 2016 standard keeps the ideas but folds repricing and yield curve risk into one, gap risk, split into parallel and non-parallel risk (SRP31.2). The words changed; the four questions did not.

Key takeaways

Interest rate risk in the banking book has four sources: repricing (gap), yield curve, basis and option risk; the Basel standard groups the first two as gap risk.
RiskAtoms Bank is funded by slow-moving deposits and holds floating assets, so its NII rises with rates: +£91.7m in year 1 for +100bp.
Shape matters: the steepener raises long rates yet cuts year-1 NII by £191.6m, because NII lives at the short end.
Basis risk needs no change in Bank Rate: SONIA 25bp below it costs £28.9m a year on a net £13.2bn SONIA position.
Options are asymmetric: prepayment costs the bank whether rates rise or fall, because the customer chooses.

Reaction

Check what stuck

Glossary

Repricing (gap) risk: Repricing risk: the risk from timing differences in when assets and liabilities mature or reset their rates. Called gap risk in the Basel standard.
Yield curve risk: Yield curve risk: the risk that the curve changes shape (steepens, flattens, twists), so short and long rates move by different amounts.
Basis risk: Basis risk: the risk that rates on instruments that reprice at the same time, but off different indices, move by different amounts.
Option risk: Option risk: the risk from choices the bank's customers (or the bank) can make that change the amount or timing of cash flows, such as prepaying a mortgage.
Automatic option: Automatic option: one exercised whenever it pays, like a bought interest rate cap or a contractual floor on a rate.
Behavioural option: Behavioural option: one exercised by customers for many reasons, not only rates, such as prepaying a mortgage on moving house or withdrawing a deposit.
Prepayment: Prepayment: repaying a loan, in full or in part, before its contractual date.
Conditional prepayment rate (CPR): Conditional prepayment rate (CPR): the share of an outstanding loan balance repaid early in a year.
SONIA: SONIA: the Sterling Overnight Index Average, the benchmark overnight interest rate for sterling.

Deep Dives & Origins

Deep Dives

Basel Committee on Banking Supervision, Principles for the Management and Supervision of Interest Rate Risk, BIS, July 2004: sources of interest rate risk, paragraphs 13 to 16. Intermediate.
Federal Deposit Insurance Corporation, History of the Eighties: Lessons for the Future, volume 1, chapter 4, "The Savings and Loan Crisis and Its Relationship to Banking", 1997. Introductory.

Origins

Basel Committee on Banking Supervision, Basel Framework, SRP31 Interest rate risk in the banking book, paragraph 31.2, BIS, version in force from 1 January 2026.
Basel Committee on Banking Supervision, Principles for the Management and Supervision of Interest Rate Risk, BIS, July 2004, paragraphs 13 to 16.
Federal Deposit Insurance Corporation, History of the Eighties: Lessons for the Future, volume 1, chapter 4, pages 168 to 173, 1997.

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