Interest Rate Risk and Funds Transfer Pricing

Introduction

Banks transform short-term and withdrawable funding into longer-term loans and investments. This maturity transformation supports credit creation but exposes earnings and economic value to changes in interest rates. A bank may report stable current income while carrying substantial long-term value risk, or it may protect economic value while accepting temporary earnings volatility. Effective asset–liability management therefore examines both perspectives.

Interest rate risk in the banking book (IRRBB) differs from trading-book market risk. Trading positions are generally marked to market and managed over shorter horizons. Banking-book positions—including loans, deposits and held-to-collect securities—require models of repricing, customer behaviour, embedded options and transfer pricing.

Funds transfer pricing (FTP) complements risk measurement by assigning an internal funding value or cost to products. Lending units normally incur an FTP funding charge, whereas deposit-gathering units receive an FTP credit. This separates customer pricing performance from centrally managed interest rate and liquidity risks.

Learning Objectives

After studying this chapter, students should be able to:

1. Identify the principal forms of banking-book interest rate risk.
2. Calculate repricing gaps and approximate net interest income sensitivity.
3. Calculate Macaulay duration, modified duration and convexity.
4. estimate changes in economic value using duration-based measures.
5. Interpret parallel and non-parallel yield-curve movements.
6. Explain behavioural assumptions affecting deposits, prepayments and early withdrawals.
7. Apply matched-maturity FTP to lending and deposit products.
8. Evaluate governance, modelling and strategic responses to interest rate risk.

1. Sources of Interest Rate Risk

Interest rate risk arises when assets, liabilities and off-balance-sheet instruments respond differently to market rates.

1.1 Repricing risk

Repricing risk results from differences in the timing of rate resets or maturities. A five-year fixed-rate mortgage funded by a three-month deposit has a long asset repricing period and a short liability repricing period. Funding costs may increase before mortgage income changes.

1.2 Yield-curve risk

Yield-curve risk arises because rates at different maturities do not always move by the same amount. The curve may steepen, flatten, invert or change curvature. A hedge based only on a parallel shift may therefore leave material residual risk.

1.3 Basis risk

Basis risk occurs when instruments linked to different reference rates do not move identically. For example, a loan priced against a three-month interbank rate may be funded through deposits whose administered rates respond only partially to wholesale market rates.

1.4 Optionality risk

Customer and contractual options alter expected cash flows. Important examples include:

• mortgage prepayment;
• early withdrawal of term deposits;
• depositors’ ability to move balances between accounts;
• loan-rate caps and floors;
• commitments that customers may draw when market conditions change.

Optionality is often asymmetric. Mortgage borrowers tend to prepay more rapidly when rates decline, limiting the lender’s price appreciation and forcing reinvestment at lower yields.

1.5 Behavioural risk

Many products lack fixed contractual repricing dates. Non-maturity deposits may remain with a bank for years even though they are legally withdrawable immediately. Their effective maturity and sensitivity must therefore be estimated from observed behaviour rather than contractual terms alone.

Figure: Interest rate risk sources affect both short-term earnings and long-term economic value.

2. Repricing Gap and Earnings Sensitivity

2.1 Repricing gap

A repricing schedule allocates rate-sensitive assets (RSA), rate-sensitive liabilities (RSL) and relevant off-balance-sheet positions to time buckets based on the next contractual or behavioural repricing date.

Here, G_i is the repricing gap in bucket i, while RSA_i and RSL_i are currency amounts repricing within that bucket. A positive gap means more assets than liabilities reprice; a negative gap means more liabilities reprice.

The cumulative gap through bucket k is:

2.2 Worked repricing schedule

Suppose a bank prepares the following behavioural schedule, in millions of currency units:

The one-year cumulative gap is -70 + 40 = -30 million. If all positions in the first year reprice immediately and fully following a parallel 1 percentage-point increase, the simplified annual effect is:

Thus annual net interest income (NII) would fall by approximately 0.3 million under the highly simplified assumptions.

2.3 Limitations of the gap approximation

The basic formula assumes that:

• all instruments within a bucket reprice at the same time;
• asset and liability rates change by the full market-rate shock;
• balances remain constant;
• no new business occurs;
• customer options do not change cash flows;
• the yield curve moves in parallel.

These assumptions rarely hold exactly. A more detailed earnings simulation models instrument-level cash flows, projected volumes, repricing lags, floors and customer-rate pass-through.

For instrument j, an approximate contribution over horizon H is:

where B_j is the average balance in currency units, β_j is the pass-through or deposit beta, ∆r_j is the relevant market-rate change, and τ_j is the fraction of the horizon for which the new rate applies. Signs must reflect whether the item produces interest income or interest expense.

A deposit beta of 0.40 means that a 1 percentage-point market-rate increase is expected to raise the deposit rate by 0.40 percentage points. Betas are empirical assumptions, not universal constants, and may differ in rising and falling rate environments.

3. Present Value, Duration and Convexity

3.1 Present value

For a fixed-income instrument with cash flows at equally spaced periods, price is:

Here, P is price, CF_t is the cash flow at the end of period t, y is the effective yield per period, and n is the number of periods. The formula assumes a single per-period discount rate. A term structure should instead discount each cash flow using its maturity-specific spot rate.

3.2 Macaulay and modified duration

Macaulay duration is the present-value-weighted average time to receive cash flows:

If periods are years, D_Mac is measured in years. For annual compounding, modified duration is:

More generally, with nominal annual yield y^(m) compounded m times per year:

Modified duration gives the first-order price sensitivity to a small yield change:

The yield change must be expressed as a decimal; for example, 100 basis points equals 0.01.

3.3 Convexity

Duration gives a linear approximation even though the price–yield relationship is curved. For annual cash flows and annual effective yield, modified convexity is:

When periods are years, C is measured in years squared. The duration–convexity approximation is:

This discrete-cash-flow formula applies to option-free fixed cash flows. Instruments with embedded options may exhibit changing or even negative effective convexity and should be measured using scenario-based effective duration and convexity.

3.4 Worked duration and convexity calculation

Consider a two-year bond with a face value of 100, a 5% annual coupon and a 5% annual yield. Its cash flows are 5 after one year and 105 after two years.

Macaulay duration is:

Modified duration is:

Convexity is:

For a yield increase of 1 percentage point, ∆y = 0.01:

The exact price at a 6% yield is approximately 98.167, so the convexity-adjusted estimate is highly accurate for this small change.

4. Economic Value of Equity

Economic value of equity (EVE) is the present value of asset cash flows minus the present value of liability cash flows, including relevant off-balance-sheet positions:

Unlike accounting equity, EVE is a forward-looking valuation measure sensitive to the timing and discounting of expected cash flows.

4.1 Duration gap

Under the restrictive assumptions of a common yield and approximately parallel yield changes, the Macaulay duration gap is:

Here, D_A and D_L are the Macaulay durations of assets and liabilities, while A and L are their present values. Liability duration is weighted by the liability-to-asset ratio L/A, not by A/L.

The approximate EVE change is:

This form assumes annual compounding, a common initial yield y, a small parallel shock and fixed cash flows. Using modified durations directly gives the more general first-order expression:

4.2 Worked duration-gap example

Assume:

• assets A = 1,000 million;
• liabilities L = 900 million;
• asset Macaulay duration D_A = 3.8 years;
• liability Macaulay duration D_L = 2.1 years;
• common yield y = 5%.

For a parallel increase of 100 basis points:

The positive duration gap means assets have greater rate sensitivity than liability funding after scaling. Rising rates therefore reduce EVE, while falling rates increase it, subject to the limitations of duration and behavioural assumptions.

4.3 Economic value versus earnings

NII and EVE answer different questions:

A strategy can improve one measure while worsening the other. Extending fixed-rate funding may stabilize NII but create a short-duration liability position whose value rises significantly when rates decline.

5. Yield-Curve Scenarios and Key-Rate Sensitivity

A parallel shift changes all maturities by the same amount. Real market movements are often non-parallel:

• Steepening: long-term rates rise relative to short-term rates.
• Flattening: the spread between long- and short-term rates narrows.
• Inversion: short-term rates exceed long-term rates.
• Curvature change: medium-term rates move differently from both ends.

Key-rate duration measures price sensitivity to a change around a selected maturity while holding other curve points approximately constant. For key rate k:

Here, P_k⁺ and P_k^- are prices after equal upward and downward shocks at key rate k, P₀ is initial price, and ∆y_k is the decimal shock size. This central-difference measure is model-dependent because the local curve shock must be interpolated across adjacent maturities.

For small curve changes, portfolio value sensitivity can be approximated by:

Key-rate analysis reveals mismatches concealed by total duration. Two portfolios can have equal modified duration but very different exposures to two-year and ten-year rates.

Banks should combine deterministic supervisory shocks with institution-specific scenarios. Scenarios may include rapid tightening, prolonged low rates, yield-curve inversion, deposit competition, changing prepayment rates and basis widening.

6. Funds Transfer Pricing

6.1 Purpose and economic logic

FTP assigns an internal funding rate to each product or transaction. It aims to:

• separate customer business performance from treasury risk management;
• incorporate term funding and liquidity costs into pricing;
• reward stable funding sources;
• support product, channel and customer profitability analysis;
• discourage business units from creating unpriced structural risk.

Under matched-maturity FTP, treasury notionally funds each asset for a maturity matching its expected cash flows and notionally invests the funds generated by each liability.

Figure: Lending units incur FTP funding charges, while deposit units receive FTP credits.

6.2 Loan and deposit margins

For a loan, a simplified business-unit margin is:

A complete profitability measure may also deduct allocated capital and overhead charges. The lending unit does not receive an FTP credit for originating the loan; it incurs the internal funding charge.

For a deposit:

The FTP credit rewards the unit for providing funding to treasury. The credit should reflect the deposit’s stable or behavioural maturity rather than automatically using its overnight contractual maturity.

6.3 Constructing an FTP curve

An FTP rate may contain several components:

Not every institution displays these components separately, and double counting must be avoided. The reference curve may be based on risk-free or swap rates. Bank-specific funding spreads represent the institution’s marginal unsecured or secured funding costs. Liquidity premiums compensate for term funding requirements. Optionality adjustments reflect prepayment or withdrawal rights.

6.4 Numerical FTP application

Suppose treasury assigns a five-year fixed-rate mortgage:

• five-year reference rate: 4.20%;
• liquidity premium: 0.35%;
• prepayment option charge: 0.25%;
• no additional basis adjustment.

The FTP funding charge is:

If the customer mortgage rate is 6.40%, the lending spread before credit and operating costs is:

For a stable deposit receiving a 3.60% FTP credit and paying the customer 2.00%, the deposit unit earns 1.60% before direct operating costs.

6.5 FTP design choices and potential distortions

Poor FTP design can encourage undesirable behaviour. A single average funding rate may make long-term lending appear too profitable and stable deposits insufficiently valuable. Excessively complex systems, however, can become opaque and difficult to challenge.

A sound framework requires:

• matched maturity or matched expected cash-flow profiles;
• consistent treatment of embedded options;
• transparent ownership of model assumptions;
• periodic recalibration to observable market funding costs;
• independent validation and reconciliation to treasury results;
• controls against retrospective changes that manipulate performance.

7. Illustrative Integrated Case: Meridian Community Bank

Background

Meridian Community Bank is a fictional institution with 1,000 million in assets and 900 million in liabilities. Rapid growth in five-year fixed-rate mortgages has been funded largely through short-term deposits. Management is concerned that rising rates may reduce both earnings and economic value.

Problem

The one-year repricing schedule shows 420 million of RSA and 500 million of RSL. Asset and liability Macaulay durations are 3.8 and 2.1 years respectively. Mortgage pricing has historically used the average deposit cost rather than a matched-term FTP rate.

Analysis

The one-year gap is:

Under an immediate, parallel 1 percentage-point increase with full pass-through, simplified annual NII sensitivity is:

Using the duration assumptions and a 5% common yield, the duration gap is 1.91 years and estimated EVE loss is 18.19 million, as calculated earlier. Both measures indicate exposure to rising rates, although they represent different horizons.

Treasury then introduces the 4.80% mortgage FTP charge derived above. A mortgage priced at 6.40% produces only 1.60% before expected credit losses, servicing costs and capital charges. The former average funding cost of 3.20% had overstated product profitability by 1.60 percentage points.

Approach and solution

Meridian adopts four measures:

1. Price new fixed-rate mortgages using matched-maturity FTP.
2. Increase the value assigned to demonstrably stable deposit balances.
3. Use pay-fixed, receive-floating swaps to reduce exposure to rising rates, subject to counterparty, collateral and accounting analysis.
4. Set separate board limits for NII sensitivity, EVE sensitivity and key-rate concentrations.

Outcome

The revised framework does not eliminate risk. Instead, it makes the cost and ownership of risk visible. Mortgage volumes moderate because customer pricing now reflects term funding and optionality costs. Treasury centralizes the remaining structural exposure and can decide whether to hedge, retain or offset it through balance-sheet actions.

Learning points

• A positive accounting spread does not necessarily imply adequate risk-adjusted profitability.
• NII and EVE must be assessed together.
• Lending units incur FTP funding charges; deposit units receive FTP credits.
• Behavioural assumptions can materially alter measured risk.
• Hedging decisions should consider basis, liquidity, counterparty and accounting consequences.

8. Governance, Regulation and Model Risk

The board should approve the institution’s interest rate risk appetite, material limits and escalation procedures. An asset–liability committee typically oversees exposures, funding strategy, product pricing and hedging. Independent risk management should challenge treasury and business assumptions, while internal audit evaluates governance and control effectiveness.

The Basel Committee’s IRRBB framework emphasizes both EVE and earnings-based measures. Standardized supervisory scenarios include parallel, steepening, flattening and short-rate shocks. The Basel framework identifies banks with excessive EVE decline relative to Tier 1 capital for enhanced supervisory attention; exact requirements and calibrations depend on jurisdictional implementation.

Major model risks include:

• unstable deposit betas and decay rates;
• incorrect prepayment estimates;
• aggregation within broad repricing buckets;
• inappropriate discount curves;
• omitted basis relationships;
• reliance on historical periods unlike current conditions;
• data quality and product-classification errors.

Back-testing should compare predicted repricing, attrition and prepayment behaviour with actual outcomes. Sensitivity analysis should test assumptions independently, and stress testing should consider behavioural changes during competitive or liquidity pressure.

Ethically, FTP should not be manipulated to reward preferred units or conceal losses. Model changes require documentation, approval and consistent application. Customer pricing must also comply with consumer protection, fairness and disclosure requirements.

9. Technology and Contemporary Developments

Modern asset–liability management systems integrate transaction-level cash flows, market curves, behavioural models and scenario engines. Machine learning can assist in estimating deposit attrition, beta behaviour and mortgage prepayments. Nevertheless, predictive accuracy can deteriorate after regime changes, and complex models may be difficult to explain.

Responsible use requires interpretable outputs, monitored data quality, model validation and human oversight. Emerging priorities include rapidly changing deposit competition, transition to risk-free reference rates, climate-related effects on loan cash flows, intraday liquidity interaction and more granular customer-level behavioural analysis.

10. Practical Best Practices

Banks should:

1. measure both NII and EVE under multiple scenarios;
2. use granular maturity and repricing data;
3. separate contractual from behavioural assumptions;
4. evaluate parallel, basis and non-parallel curve shocks;
5. price embedded options explicitly;
6. align FTP with marginal term funding and liquidity costs;
7. validate models and stress key assumptions;
8. assign risk ownership clearly between treasury and business units;
9. monitor limit utilization and hedge effectiveness;
10. communicate model uncertainty rather than presenting estimates as exact forecasts.

Chapter Summary

Interest rate risk results from mismatched repricing, yield-curve changes, basis relationships, embedded options and customer behaviour. Repricing gaps provide a useful first approximation of earnings sensitivity but ignore timing, pass-through and behavioural complexity. NII simulation therefore supplements static gap analysis.

Duration measures first-order price sensitivity, while convexity improves estimates for larger yield changes. Duration gap connects asset and liability sensitivities to approximate EVE changes, with liability duration correctly weighted by the liability-to-asset ratio. Key-rate duration and scenario analysis are needed when the yield curve moves non-parallelly.

FTP allocates funding, liquidity and optionality costs to products. Lending units incur funding charges, whereas deposit units receive credits for supplying funds. A robust FTP system improves pricing and performance measurement while centralizing structural risk in treasury. Effective management requires sound governance, validated behavioural models, stress testing and simultaneous attention to earnings and economic value.

Key Terms

Basis risk: Risk that rates on related assets, liabilities or hedges move by different amounts.

Convexity: The second-order sensitivity of price to yield changes, measured in time squared under standard fixed-cash-flow formulas.

Deposit beta: The proportion of a market-rate change passed through to a deposit rate.

Duration gap: Asset duration minus liability duration scaled by the liability-to-asset ratio, D_A - (L/A)D_L.

Economic value of equity (EVE): Present value of asset cash flows minus liability cash flows, adjusted for off-balance-sheet positions.

Effective duration: Scenario-based price sensitivity used when cash flows change as interest rates change.

Funds transfer pricing (FTP): Internal pricing system that allocates funding and liquidity value or cost to products and business units.

Interest rate risk in the banking book (IRRBB): Risk to earnings or economic value caused by interest-rate movements in non-trading positions.

Key-rate duration: Sensitivity of value to a change around a specified yield-curve maturity.

Macaulay duration: Present-value-weighted average time until cash flows are received.

Matched-maturity FTP: Transfer pricing based on the maturity or expected cash-flow profile of a transaction.

Modified duration: First-order percentage price sensitivity to a small yield change.

Net interest income (NII): Interest income earned minus interest expense incurred over a period.

Non-maturity deposit: Deposit without a fixed contractual maturity, requiring behavioural modelling.

Optionality risk: Risk arising because contractual or customer choices alter cash-flow timing.

Repricing gap: Rate-sensitive assets minus rate-sensitive liabilities within a time bucket.

Repricing risk: Risk caused by differences in the timing of asset and liability rate resets or maturities.

Yield-curve risk: Risk arising from changes in the level, slope or curvature of interest rates across maturities.

Review Questions

Short Answer Questions

1. Distinguish repricing risk from basis risk.
2. What does a negative one-year repricing gap indicate?
3. Why is modified duration more directly useful for price sensitivity than Macaulay duration?
4. Why do non-maturity deposits require behavioural assumptions?
5. What is the principal purpose of matched-maturity FTP?

Long Answer Questions

1. Explain the strengths and limitations of repricing-gap analysis.
2. Derive the duration–convexity approximation and discuss its assumptions.
3. Compare the earnings and economic-value perspectives of interest rate risk.
4. Explain how FTP supports product pricing, performance measurement and risk centralization.
5. Discuss governance and model-risk controls required for an effective IRRBB framework.

Analytical / Application Questions

1. A bank has one-year RSA of 360 million and RSL of 440 million. Estimate the simplified annual NII effect of a 75-basis-point increase and critically assess the assumptions.
2. Using assets of 800 million, liabilities of 720 million, asset duration of 4.2 years and liability duration of 2.8 years, calculate duration gap and interpret the direction of EVE exposure.
3. Design an FTP rate for a seven-year fixed-rate loan, identifying appropriate reference, liquidity, basis and optionality components and explaining how double counting would be prevented.

Multiple Choice Questions with Answers

Question 1

A bank has rate-sensitive assets of 240 million and rate-sensitive liabilities of 300 million in the one-year bucket. What is its one-year repricing gap?

A. +60 million

B. −60 million

C. +540 million

D. −540 million

Correct Answer: B. −60 million

Question 2

A bank has a one-year cumulative gap of −40 million. Under the simplified gap model, what is the approximate annual NII effect of an immediate 50-basis-point rate increase?

A. An increase of 0.20 million

B. A decrease of 0.20 million

C. A decrease of 2.00 million

D. No change

Correct Answer: B. A decrease of 0.20 million

Question 3

A bond has Macaulay duration of 4.20 years and an annual effective yield of 5%. What is its modified duration?

A. 3.80 years

B. 4.00 years

C. 4.20 years

D. 4.41 years

Correct Answer: B. 4.00 years

Question 4

For the two-year 5% coupon bond described in the chapter, D_mod=1.859410 and C=5.269. Using a 1 percentage-point yield increase, what is the convexity-adjusted estimated price if the initial price is 100?

A. 98.141

B. 98.167

C. 98.594

D. 101.859

Correct Answer: B. 98.167

Question 5

A bank has assets of 1,000 million, liabilities of 900 million, asset duration of 3.8 years and liability duration of 2.1 years. What is its duration gap?

A. 1.70 years

B. 1.90 years

C. 1.91 years

D. 2.11 years

Correct Answer: C. 1.91 years

Question 6

Which measure is most directly designed to identify sensitivity to non-parallel movements at selected yield-curve maturities?

A. Cumulative repricing gap

B. Key-rate duration

C. Deposit beta

D. Accounting equity ratio

Correct Answer: B. Key-rate duration

Question 7

Under a conventional matched-maturity FTP system, how is a newly originated fixed-rate loan normally treated?

A. The lending unit receives an FTP credit

B. The lending unit incurs an FTP funding charge

C. The deposit unit incurs the loan's credit loss

D. Treasury ignores the loan's maturity

Correct Answer: B. The lending unit incurs an FTP funding charge

Question 8

A deposit unit receives an FTP credit of 3.60% and pays customers 2.00%. Ignoring direct costs, what is its deposit margin?

A. 1.60%

B. 2.00%

C. 3.60%

D. 5.60%

Correct Answer: A. 1.60%

Question 9

A loan is linked to a three-month interbank rate while its funding cost follows an administered deposit rate. The risk that these rates move differently is primarily:

A. Credit risk

B. Basis risk

C. Settlement risk

D. Operational risk

Correct Answer: B. Basis risk

Question 10

Which statement correctly describes the duration-gap formula?

A. Liability duration is multiplied by the asset-to-liability ratio

B. Asset duration is multiplied by the liability-to-asset ratio

C. Liability duration is multiplied by the liability-to-asset ratio

D. Asset and liability durations are added without scaling

Correct Answer: C. Liability duration is multiplied by the liability-to-asset ratio