Swaps and Credit Derivatives

Introduction

A swap is a contractual agreement to exchange specified cash flows over time. Swaps allow organizations to transform interest-rate, currency, commodity-price or asset-return exposures without necessarily selling the underlying assets or refinancing existing liabilities. Credit derivatives transfer credit risk separately from ownership of the underlying debt.

Swaps are widely used by banks, corporations, investment funds and governments. Their flexibility is valuable, but it introduces counterparty credit exposure, liquidity risk, model risk, collateral requirements and potentially significant termination costs. Sound application therefore requires both accurate valuation and effective governance.

Learning Objectives

After studying this chapter, students should be able to:

1. Explain the contractual structure of interest-rate, currency, commodity and total-return swaps.
2. Value an interest-rate swap using discounted cash flows and bond-equivalent methods.
3. Apply comparative advantage and quality-spread differentials cautiously.
4. Value currency and commodity swaps while maintaining correct cash-flow directions.
5. Analyze total-return swaps using scenario analysis and no-arbitrage valuation principles.
6. Explain credit default swaps and estimate fair CDS spreads under stated assumptions.
7. Assess counterparty exposure, collateralization, close-out and termination risk.
8. Evaluate accounting, regulatory, governance and ethical considerations.

1. Swap Fundamentals

A swap normally contains two legs. A fixed leg makes payments determined by an agreed fixed rate or price. A floating leg depends on a market reference such as the Secured Overnight Financing Rate (SOFR), an exchange rate, a commodity index or an asset's total return.

The notional principal determines payment amounts but is not normally exchanged in a standard interest-rate swap. Currency swaps are an important exception because principal amounts are commonly exchanged at inception and re-exchanged at maturity.

For one settlement period, a net interest payment may be written as:

Here, N is the notional principal in currency units, α is the year fraction, R_floating is the floating rate set under the contract, and K is the fixed swap rate. The expression is positive from the perspective of the floating-rate receiver. Actual contracts may exchange gross payments, although net settlement is common when legally enforceable.

Figure: Contractual cash flows in a standard fixed-for-floating interest-rate swap.

At inception, a market-rate swap generally has approximately zero value to both parties. After inception, changes in market rates, exchange rates, commodity prices, credit quality and funding conditions cause its value to become positive for one party and negative for the other.

2. Interest-Rate Swaps

2.1 Structure and risk transformation

In a plain-vanilla interest-rate swap, one party pays a fixed rate and receives a floating rate in the same currency. The other party receives fixed and pays floating.

A company with floating-rate debt can synthetically create fixed-rate debt by entering a pay-fixed, receive-floating swap. Ignoring differences in reset dates and reference rates:

Conversely, fixed-rate debt combined with a receive-fixed, pay-floating swap creates synthetic floating-rate debt. If the debt and swap use different reference rates, tenors or reset dates, the hedge retains basis risk.

A fixed-rate payer generally gains when market fixed swap rates rise because its contractual fixed rate becomes relatively favorable. A fixed-rate receiver generally gains when market rates fall.

2.2 Valuation by leg comparison

The value to the fixed-rate receiver is:

B_fixed and B_floating are the present values of the remaining fixed and floating legs. The fixed payer has the opposite value.

Under a multi-curve framework, forward floating rates are projected from an appropriate reference-rate curve and cash flows are discounted using the collateral-consistent discount curve. For payment dates t_i, the general fixed-leg present value is:

The added principal is a valuation device that permits comparison with a floating-rate note; swap principal itself is not exchanged. Here, D(0,t_i) is the discount factor to date t_i, α_i is the fixed-leg year fraction, and K is the annualized fixed rate.

The projected floating-leg value is:

F_i is the forward reference rate for period i. When the next floating coupon is already fixed, that known coupon must replace its forward estimate.

For a spot-starting swap valued at inception, the fair fixed rate is:

This formula assumes aligned payment dates and a conventional fixed-for-floating structure. In a single-curve framework it simplifies to K^* = [1-D(0,t_n)]/∑α_iD(0,t_i). That simplification should not be applied indiscriminately in a multi-curve market.

2.3 Worked example: fixed receiver

A two-year annual-pay swap has a notional of $800,000. The fixed receiver receives 4% annually and pays floating. The next floating coupon has already been fixed at 5%, or $40,000. Immediately after the next payment, the floating-rate note resets to par. The relevant discount factors are:

The fixed coupon is $32,000. Therefore:

Because the floating instrument will be worth $800,000 immediately after the known $40,000 coupon is paid, its current value is:

Thus:

The fixed receiver has a liability of $8,800, while the fixed payer has an asset of $8,800. The result is consistent with the fixed receiver's obligation to pay a relatively high next floating coupon.

3. Comparative Advantage and the Quality-Spread Differential

The traditional comparative-advantage explanation argues that two borrowers may obtain financing in markets where each has a relative borrowing advantage and then use a swap to reach the desired exposure.

Consider the following actual borrowing quotations:

The fixed-rate borrowing differential is 7.025.0 = 2.0%, while the floating-rate differential is 1.220.4 = 0.8%. The quality-spread differential is therefore:

A has a comparative advantage in fixed-rate borrowing, while B has a comparative advantage in floating-rate borrowing. Suppose A wants floating exposure and B wants fixed exposure. A borrows at 5.0%, B borrows at SOFR + 1.2%, and they enter a swap in which A receives 5.2% fixed and pays SOFR.

A's effective cost is:

This saves A 0.6% relative to direct floating borrowing at SOFR + 0.4%. B's effective cost is:

B also saves 0.6% relative to direct fixed borrowing at 7.0%. The total 1.2% saving equals the QSD.

This model is pedagogically useful but incomplete. Apparent savings may reflect differences in credit risk, embedded options, liquidity, maturity, collateral and reference rates. A swap does not eliminate the underlying borrowers' default risks, and dealer fees may absorb part of the theoretical gain.

4. Currency Swaps

4.1 Contractual cash-flow directions

A currency swap exchanges cash flows denominated in different currencies. Principal is commonly exchanged at inception using the spot exchange rate and reversed at maturity. Cash-flow directions must be traced consistently.

Suppose a US company needs €9 million and has raised $10 million. At inception it pays $10 million and receives €9 million. During the contract it pays euro interest and receives dollar interest. At maturity it repays €9 million and receives $10 million. Initial principal exchanges are opposite in direction to the subsequent principal repayments.

If the initial spot rate is $1.111111 per euro, the exchanged principals have equal initial value:

Consequently, the initial principal exchange contributes zero net value when principals are matched at spot. A complete inception valuation must nevertheless include it explicitly.

Currency swaps may be fixed-for-fixed, fixed-for-floating or floating-for-floating. They hedge exchange-rate risk but may leave interest-rate, basis, counterparty and liquidity risks.

4.2 Valuation

A fixed-for-fixed currency swap can be valued as the difference between two currency-denominated bonds. From the perspective of a party receiving US dollars and paying euros:

B_USD is the dollar present value of remaining dollar receipts, B_EUR is the euro present value of remaining euro payments, and S_t is the spot exchange rate in dollars per euro. Each leg must first be discounted using an appropriate curve for its currency. Cross-currency basis and collateral currency can materially affect professional valuation.

4.3 Worked example

Assume the dollar value of the remaining dollar receipts, including principal, is $10.30 million. The euro value of the remaining euro payments is €8.70 million, and the spot rate is $1.12 per euro. Then:

The swap is worth $556,000 to the party receiving dollars and paying euros. It is worth −$556,000 to the opposite party, before valuation adjustments.

5. Commodity Swaps

A commodity swap exchanges a fixed commodity price for a floating market price. Physical delivery is usually unnecessary because differences are settled financially.

For quantity Q and settlement price P_floating, the payment to the floating-price receiver is:

The units must be consistent. If quantity is measured in barrels and prices are dollars per barrel, the settlement is in dollars.

A manufacturer that consumes fuel may pay fixed and receive floating. Higher spot or index prices generate swap receipts that offset higher physical purchase costs. A producer may receive fixed and pay floating to stabilize selling prices.

Example. An airline hedges 100,000 barrels of fuel with a fixed price of $82 per barrel. The contractual monthly average floating price is $87.50. Its receipt is:

The hedge may be imperfect if the airline buys jet fuel but the swap references crude oil. This difference is commodity basis risk. Location, grade, timing and averaging conventions can also create basis exposure.

Commodity-swap value is the discounted value of expected contractual settlements under market-consistent forward prices, not forecasts chosen solely by management:

Here, F_i is the market forward price for settlement i, K_i is the contractual fixed price, and Q_i is the contractual quantity. This expression assumes that the quoted forwards match the contract's commodity, location, quality and averaging terms.

6. Total-Return Swaps

A total-return swap (TRS) transfers the economic return on a reference asset without transferring its legal ownership. The total-return receiver obtains price appreciation and distributions, such as interest or dividends, and pays a financing return. If the asset's total return is negative, the total-return receiver pays the loss as well as the financing amount.

For a settlement period, an illustrative net payment to the total-return receiver is:

r_price is the reference asset's percentage price change, y_income is its distribution yield for the period, r_reference is the financing reference rate, and m is the contractual financing margin. The formula is a realized settlement calculation, not a general valuation formula.

Scenario calculation. A TRS references a $10 million bond portfolio. During the year, the portfolio appreciates by 4% and pays income of 1%. The financing rate is 3.2% plus a 1.0% margin. The total-return receiver obtains $500,000 of asset return and pays $420,000 of financing, producing a net receipt of $80,000.

A TRS should not be valued by merely discounting management's subjective expected asset return. Consistent valuation requires either:

• a replicating portfolio and no-arbitrage approach; or
• discounted contractual cash flows under a risk-neutral, collateral-consistent pricing measure.

Professional valuation must also account for asset funding costs, repo rates, dividends, credit events, collateral, counterparty risk and contract-specific termination terms. A newly negotiated market-rate TRS usually has a value close to zero at inception.

TRSs provide leverage and market access but can obscure economic ownership and concentrated exposures. The collapse of highly leveraged counterparties has demonstrated the importance of consolidated position reporting across dealers.

7. Credit Default Swaps

7.1 Structure

A credit default swap transfers the credit risk of a reference entity or obligation. The protection buyer pays a periodic premium, called the CDS spread. The protection seller makes a payment if a contractually defined credit event occurs.

Common credit events include bankruptcy, failure to pay and restructuring, subject to contract definitions. Settlement may be physical, involving delivery of eligible debt, or cash-based using a post-default auction price.

If the notional is N and the recovery rate is R, an approximate protection payment is:

For a $5 million CDS and a recovery rate of 35%, the payment is $3.25 million.

Buying a CDS does not necessarily remove every credit-related risk. The buyer retains counterparty risk to the protection seller, documentation risk, basis risk and the possibility that an economic loss does not satisfy the legal credit-event definition.

7.2 Fair CDS spread

Let Q(t_i) denote the risk-neutral probability of survival to date t_i, D(0,t_i) the discount factor, α_i the premium year fraction and R the assumed recovery rate. Ignoring premium accrual on default for simplicity, the premium-leg present value is:

The protection-leg present value under a discretized default model is:

The fair spread s equates the two present values. Operational CDS models also include accrued premium upon default and more precise default timing.

Under the special assumptions of a constant hazard rate λ, constant recovery, continuous premiums and similar discounting effects, the spread is approximately:

If λ = 2% and R = 40%, the approximate spread is 1.2%, or 120 basis points. This is a special approximation, not a universal identity.

7.3 Uses and limitations

CDSs are used to hedge loan or bond exposure, express credit views, diversify credit portfolios and estimate market-implied default risk. Limitations include illiquidity, uncertain recovery, jump-to-default risk, wrong-way risk and divergence between bond and CDS spreads. A speculative CDS position may also create incentives that conflict with cooperative debt restructuring.

8. Counterparty Exposure and Termination Risk

Unlike a funded bond, an over-the-counter derivative usually creates changing replacement-cost exposure. Current exposure is:

where V is the derivative's current value from the reporting entity's perspective. Potential future exposure measures how large positive exposure could become over a specified horizon and confidence level.

Key controls include:

• Netting: Enforceable close-out netting combines positive and negative values under a master agreement.
• Collateral: Variation margin covers current exposure; initial margin protects against changes during close-out.
• Central clearing: A central counterparty becomes buyer to every seller and seller to every buyer for eligible standardized contracts.
• Limits and monitoring: Institutions establish counterparty, sector, tenor and wrong-way-risk limits.
• Valuation adjustments: Credit valuation adjustment (CVA) reflects expected loss from counterparty default. Debit valuation adjustment (DVA), funding valuation adjustment (FVA) and margin valuation adjustment may also be relevant, subject to institutional policy and accounting requirements.

Wrong-way risk occurs when exposure increases as the counterparty's credit quality deteriorates. For example, protection purchased from a highly correlated financial institution may be least reliable during a systemic crisis.

Termination risk

Early termination may follow default, illegality, tax events, covenant breaches or voluntary break clauses. The close-out amount depends on replacement value, unpaid amounts, collateral and contractual methodology. A company may face a large cash payment precisely when market conditions are unfavorable.

Termination risk should therefore be assessed using stress tests that combine market movements, collateral calls, reduced liquidity and counterparty default. Legal review of the ISDA Master Agreement, schedule and credit support annex is essential.

9. Illustrative Integrated Case: Meridian Manufacturing

Background

Meridian Manufacturing is a fictional European industrial company. It has €40 million of floating-rate debt, expects to buy copper over the next two years and owns a $12 million bond portfolio financed in euros. Management is also concerned about the credit quality of a major customer whose five-year notes it holds.

Problem

Rising euro interest rates would increase debt-service costs. Higher copper prices would reduce production margins. The dollar bond portfolio creates both asset-return and currency exposure. A customer default could create a material loss. Management wants protection but must avoid excessive collateral and termination risk.

Analysis and approach

1. Interest-rate exposure: Meridian enters a pay-fixed, receive-floating euro interest-rate swap for €30 million. This transforms most of the floating debt into synthetic fixed-rate debt while leaving €10 million floating for flexibility.
2. Commodity exposure: It pays a fixed copper price and receives the contractual copper index on 60% of forecast purchases. Hedging less than 100% reduces the danger of becoming over-hedged if production falls.
3. Dollar bond exposure: Rather than treating subjective return forecasts as value, Meridian obtains market-consistent TRS and currency-swap valuations. It uses a currency swap only for the portion of dollar cash flows considered highly probable.
4. Credit exposure: Meridian buys CDS protection matching the customer's bond seniority and maturity. Legal staff verify the reference obligation, credit-event definitions and deliverable obligations.
5. Counterparty control: Trades are divided between approved dealers, governed by enforceable netting agreements and supported by collateral. Treasury stress-tests simultaneous rate increases, copper-price shocks, euro depreciation and dealer downgrade.

Outcome

The strategy reduces earnings and cash-flow volatility without eliminating all risk. Meridian retains basis risk because its physical copper purchases do not perfectly match the swap index. It also retains counterparty and liquidity risks. The board receives reports showing gross notional, net market value, collateral, stressed exposure and potential termination payments.

Learning points

A derivative program should begin with measurable underlying exposures rather than attractive-looking trades. Hedge effectiveness depends on matching currencies, indices, maturities, quantities and legal terms. Valuation, collateral and termination liquidity are as important as the intended hedge.

10. Accounting, Regulation and Governance

Under IFRS 9, derivatives are generally measured at fair value through profit or loss unless qualifying hedge-accounting requirements are met. Hedge accounting requires formal designation and documentation of the hedging relationship, risk management objective, hedged risk and method for assessing effectiveness. IFRS 13 fair-value measurement requires market-participant assumptions and consideration of non-performance risk.

Major post-crisis regulatory reforms, including the European Market Infrastructure Regulation and US Dodd–Frank requirements, promote central clearing, trade reporting, margining and platform trading for qualifying derivatives. Rules depend on jurisdiction, entity classification and product type.

Effective governance includes independent valuation, confirmation controls, collateral reconciliation, model validation, legal review, limit monitoring and board-approved risk appetite. Compensation systems should not reward notional growth without considering tail risk and funding demands.

Technology supports real-time exposure aggregation, collateral optimization and anomaly detection. Artificial intelligence can identify unusual positions or documentation discrepancies, but it should not replace independently validated pricing models, legal judgment or accountable human approval.

11. Best-Practice Principles

1. Link every derivative to a documented exposure, mandate or investment objective.
2. Map all cash-flow directions, including principal exchanges and final repayments.
3. Use market-consistent curves and contract-specific conventions.
4. Separate realized scenario calculations from fair-value estimation.
5. Measure net exposure only where netting is legally enforceable.
6. Stress collateral and close-out liquidity, not merely accounting earnings.
7. Reconcile confirmations, valuations and collateral regularly.
8. Monitor basis, wrong-way, concentration and model risks.
9. Assess hedge performance after fees, funding costs and valuation adjustments.
10. Report economic leverage and contingent liquidity needs transparently.

Chapter Summary

Swaps transform financial exposures by exchanging contractual cash flows. Interest-rate swaps convert fixed and floating obligations and are valued as the difference between fixed and floating legs. Comparative advantage may explain some swap structures, but the quality-spread differential is meaningful only when calculated from comparable actual borrowing quotations.

Currency swaps usually exchange principal at inception and reverse the exchange at maturity; valuation requires consistent cash-flow directions and currency-specific discounting. Commodity swaps stabilize prices but can leave significant basis risk. Total-return swaps transfer an asset's economic return and may create leverage; fair valuation must use no-arbitrage or risk-neutral methods rather than subjective expected returns.

A credit default swap exchanges periodic premiums for contingent default protection. Its fair spread equates the risk-adjusted present values of the premium and protection legs. Across all derivatives, counterparty exposure, collateral, netting, wrong-way risk and termination liquidity are central management concerns. Accounting, regulation and governance require accurate fair values, documentation, control and transparent reporting.

Key Terms

Basis risk: Risk arising when a hedge and the underlying exposure do not move identically.

Central counterparty: Institution that interposes itself between clearing members and manages collateral and default procedures.

Collateral: Assets transferred or pledged to reduce derivative counterparty exposure.

Commodity swap: Contract exchanging a fixed commodity price for a floating price or index.

Comparative advantage: Relative borrowing-cost advantage used to motivate certain swap structures.

Credit default swap: Contract transferring defined credit-event risk in exchange for premiums.

Credit valuation adjustment: Adjustment reflecting the market value of counterparty default risk.

Currency swap: Contract exchanging cash flows and commonly principal in different currencies.

Discount factor: Present value of one currency unit payable at a future date.

Floating leg: Swap leg whose payments depend on a reference rate, price or return.

Hazard rate: Conditional default intensity used in credit-risk models.

Interest-rate swap: Contract exchanging fixed and floating interest payments in one currency.

Netting: Legally enforceable offsetting of contractual amounts or close-out values.

Notional principal: Reference amount used to calculate derivative payments.

Potential future exposure: Estimate of possible future positive replacement cost.

Quality-spread differential: Difference between fixed-rate and floating-rate borrowing differentials.

Total-return swap: Contract transferring price changes and income on a reference asset.

Termination risk: Risk of adverse cash payments or losses when a derivative ends early.

Wrong-way risk: Risk that counterparty credit quality deteriorates as exposure increases.

Review Questions

Short Answer Questions

1. Distinguish the notional amount from the market value of a swap.
2. Why does a fixed-rate receiver generally benefit when market interest rates fall?
3. Explain the principal exchanges in a conventional currency swap.
4. What is commodity basis risk?
5. Distinguish current exposure from potential future exposure.

Long Answer Questions

1. Explain how an interest-rate swap can transform floating-rate debt into synthetic fixed-rate debt.
2. Derive the fair fixed rate of a standard interest-rate swap and state the assumptions required for the single-curve simplification.
3. Critically evaluate the comparative-advantage explanation of swap markets.
4. Explain the structure, valuation and major risks of a credit default swap.
5. Discuss how collateral, close-out netting and central clearing affect counterparty risk.

Analytical / Application Questions

1. A company receives fixed at 4.5% and pays floating on a $6 million annual-pay swap. Using supplied market discount factors and forward rates, calculate each leg's value and interpret the result.
2. Design a combined currency and commodity hedging strategy for an importer that buys oil in dollars but earns revenue in euros. Identify remaining basis and liquidity risks.
3. Evaluate whether an institution should terminate an out-of-the-money swap by considering replacement value, collateral release, funding costs, legal terms and stressed liquidity.

Multiple Choice Questions with Answers

Question 1

A company has floating-rate debt and wants synthetic fixed-rate debt. Which swap position most directly achieves this transformation when the debt and swap reference rates match?

A. Receive fixed and pay floating

B. Pay fixed and receive floating

C. Receive both fixed and floating

D. Pay both fixed and floating

Correct Answer: B. Pay fixed and receive floating

Question 2

All else being equal, which market movement benefits the receiver of a fixed rate in an existing interest-rate swap?

A. A fall in forward floating rates

B. A rise in forward floating rates

C. An increase in the contractual fixed rate after execution

D. An increase in the swap's notional after execution

Correct Answer: A. A fall in forward floating rates

Question 3

Borrower A can borrow at 5.0% fixed or SOFR + 0.4%; Borrower B can borrow at 7.0% fixed or SOFR + 1.2%. What is the quality-spread differential?

A. 0.8%

B. 1.2%

C. 2.0%

D. 2.8%

Correct Answer: B. 1.2%

Question 4

An interest-rate swap has a fixed-leg value of $802,200 and a floating-leg value of $811,000. What is its value to the fixed-rate receiver?

A. $8,800

B. −$8,800

C. $1,613,200

D. −$1,613,200

Correct Answer: B. −$8,800

Question 5

In a currency swap, a company pays $10 million and receives €9 million at inception. Which maturity principal exchange is contractually consistent from that company's perspective?

A. It pays $10 million and receives €9 million

B. It receives both principal amounts

C. It receives $10 million and pays €9 million

D. No principal can be exchanged at maturity

Correct Answer: C. It receives $10 million and pays €9 million

Question 6

A party receives dollar cash flows worth $10.30 million and pays euro cash flows worth €8.70 million. If the spot rate is $1.12 per euro, what is the swap value in dollars?

A. −$0.556 million

B. $0.556 million

C. $9.744 million

D. $20.044 million

Correct Answer: B. $0.556 million

Question 7

A company receives floating and pays a fixed commodity price of $82 per barrel on 100,000 barrels. If the settlement index is $87.50, what does it receive?

A. $82,000

B. $550,000

C. $8,200,000

D. $8,750,000

Correct Answer: B. $550,000

Question 8

Why is discounting management's subjective expected asset return generally inappropriate for valuing a total-return swap?

A. A TRS never contains future cash flows

B. Accounting rules prohibit every form of discounting

C. Fair valuation requires market-consistent no-arbitrage or risk-neutral inputs

D. The reference asset must always be physically delivered

Correct Answer: C. Fair valuation requires market-consistent no-arbitrage or risk-neutral inputs

Question 9

A CDS has a notional of $5 million and a recovery rate of 35%. Ignoring accrued premium, what approximate payment follows a covered credit event?

A. $1.25 million

B. $1.75 million

C. $3.25 million

D. $5.00 million

Correct Answer: C. $3.25 million

Question 10

Which situation is the clearest example of wrong-way risk?

A. Collateral increases while exposure falls

B. Exposure to a counterparty rises as that counterparty's credit quality deteriorates

C. Two independent counterparties have equal credit ratings

D. A swap's fixed and floating payments occur on the same date

Correct Answer: B. Exposure to a counterparty rises as that counterparty's credit quality deteriorates