Interest Rate Swap Schedule Generator

Financial ServicesFormal VerificationRegulatory ComplianceEdge Case Discovery

Overview

This case study demonstrates how CodeLogician ensures mathematical correctness in financial infrastructure that processes hundreds of trillions of dollars annually. We formally verify the schedule generation logic for vanilla interest rate swaps—the most traded derivative instrument in global markets.

What's at Stake

Interest rate swaps have $400+ trillion notional outstanding globally.

A bug in scheduling logic can cause:

Incorrect cash flows — paying or receiving wrong amounts on wrong dates
Margin call failures — miscalculated collateral leading to default
Regulatory breaches — EMIR and Dodd-Frank mandate accurate reporting
Systemic risk — cascading failures across interconnected counterparties

What Is an Interest Rate Swap?

The Business Problem

Imagine a company that borrowed $100 million at a floating interest rate (e.g., SOFR + 2%). Every quarter, their interest payment changes based on market rates:

Q1: Rate is 5.2% → Pay $1.3 million
Q2: Rate is 5.8% → Pay $1.45 million
Q3: Rate is 4.9% → Pay $1.225 million

This unpredictability makes budgeting extremely difficult.

The Solution: Interest Rate Swap

The company enters a swap with a bank:

Company Pays (Fixed Leg)

4.5%

Fixed rate, paid quarterly

= $1.125M per quarter

Predictable, every quarter, for the life of the swap

Bank Pays (Floating Leg)

SOFR + 2%

Variable rate, paid quarterly

= Market rate × $100M

Changes each quarter based on market

Result: The company's effective rate is now 4.5% fixed, making their budget predictable for the next 2-10 years.

The Scheduler's Job

Our software generates the payment schedule for these swaps:

All payment dates for 2-10 years
Business day adjustments (no weekend payments)
Day count fractions for interest calculations
Fixed payment amounts per period

The Critical Logic: Weekend Date Adjustment

The Simple Rule

Business Day Convention

"If a payment date falls on Saturday or Sunday, move it to the next Monday."

This sounds trivial. Banks are closed on weekends—you can't wire $1 million on Saturday.

The Hidden Complexity

But this simple rule has subtle edge cases that formal verification discovered:

Business Day Adjustment Logic

Python Implementation

def adjust_business_day_following(date: date) -> date:
    """
    Adjust a date to the following business day if it falls on a weekend.
    
    Following convention: Move forward to next business day.
    """
    weekday = date.weekday()  # 0=Monday, 6=Sunday
    
    if weekday == 5:  # Saturday
        return date + timedelta(days=2)  # Move to Monday
    elif weekday == 6:  # Sunday
        return date + timedelta(days=1)  # Move to Monday
    else:
        return date  # Weekday, no adjustment needed

Example: Normal Operation

Jan 13, 2024 (Saturday)→Jan 15, 2024 (Monday)

Jan 14, 2024 (Sunday)→Jan 15, 2024 (Monday)

Jan 15, 2024 (Monday)→Jan 15, 2024 (Monday)

Three Behavioral Regions

CodeLogician's region decomposition identified:

Region 1: Saturday → add 2 days
Region 2: Sunday → add 1 day
Region 3: Weekday → no change

Complete coverage: Every possible date falls into exactly one region

Real-World Example

Swap Contract Terms

Contract Specification

Start Date:: January 15, 2024
Maturity:: January 15, 2026
Term:: 2 years
Notional:: $10 million
Fixed Rate:: 4.5%
Frequency:: Quarterly

Fixed Leg Cash Flows

Per Quarter: $10M × 4.5% ÷ 4 = $112,500

Total Payments: 8 quarters

Total Fixed:$900,000

Generated Payment Schedule

Period	Accrual Start	Accrual End	Payment Date	Fixed Payment
1	Jan 15, 2024	Apr 15, 2024	Apr 15, 2024	$112,500
2	Apr 15, 2024	Jul 15, 2024	Jul 15, 2024	$112,500
3	Jul 15, 2024	Oct 15, 2024	Oct 15, 2024	$112,500
4	Oct 15, 2024	Jan 15, 2025	Jan 15, 2025	$112,500
5	Jan 15, 2025	Apr 15, 2025	Apr 15, 2025	$112,500
6	Apr 15, 2025	Jul 15, 2025	Jul 15, 2025	$112,500
7	Jul 15, 2025	Oct 15, 2025	Oct 15, 2025	$112,500
8	Oct 15, 2025	Jan 15, 2026	Jan 15, 2026	$112,500
Total Fixed Payments:				$900,000

All Dates Verified

✅ Every payment date is guaranteed to be a business day (Monday-Friday)
✅ Dates are strictly increasing
✅ Final payment matches maturity date (adjusted)

Regulatory Context

Why This Matters for Compliance

🇪🇺
EMIR (Europe)

European Market Infrastructure Regulation

✓ Accurate trade reporting
✓ Margin calculations
✓ Central clearing mandates

🇺🇸
Dodd-Frank (US)

Wall Street Reform Act

✓ Swap data repositories
✓ Real-time reporting
✓ Risk mitigation

📋
ISDA Definitions

Industry Standards (2006)

✓ Business day conventions
✓ Day count methods
✓ Payment calculation rules

The Audit Advantage

❌ Traditional Testing

To Auditors:

"We ran 1,000 test cases and they all passed."

Auditor's Response:

"But what about the edge cases you didn't think to test?"

✅ Formal Verification

To Auditors:

"We mathematically proved the rules hold for ALL inputs—past, present, and future."

Auditor's Response:

"That's the gold standard. Approved."

Key Results

Verification Summary

Property	Method	Result	Impact
No weekend dates	Formal proof	✅ PROVED	All inputs covered
Naive monotonicity	Formal proof	❌ REFUTED	Counterexample found
Practical monotonicity (7+ days)	Formal proof	✅ PROVED	All swaps covered
Complete path coverage	Region decomposition	✅ COMPLETE	3 regions identified
Test case generation	Automatic from regions	✅ GENERATED	3 systematic tests

Business Value

Mathematical Certainty

Not "tested on 1,000 cases" but proven correct for ALL possible inputs. This is mathematical certainty, not statistical confidence.

Edge Case Discovery

Found a subtle date collision that unit tests would likely miss. Documented for completeness even though it's practically irrelevant for swaps.

Regulatory Confidence

Auditors and regulators can review the formal proofs, not just test results. This provides unprecedented confidence in system correctness.

Complete Coverage

Region decomposition automatically generated systematic test cases covering all behavioral regions. No guesswork required.

Download the Code

Python Implementation IML Formal Model

Broader Applications

This verification approach applies to any financial calculation involving:

✅ Date Arithmetic

Payment schedules, accrual periods, settlement dates

✅ Business Day Conventions

Following, Modified Following, Preceding adjustments

✅ Day Count Fractions

ACT/360, ACT/365, 30/360 conventions

✅ Fixed Income Products

Bonds, loans, repos, forward rate agreements

✅ Derivative Contracts

Swaps, options, futures, credit default swaps

✅ Regulatory Calculations

Margin requirements, capital calculations, exposure limits

Industry Examples

Capital Markets: Bond pricing engines, yield curve construction
Clearing Houses: Settlement schedule generation, margin calculations
Corporate Treasury: Debt servicing schedules, hedge accounting
Asset Management: Portfolio analytics, performance attribution
Risk Management: VaR calculations, stress testing scenarios

Key Takeaways

Mathematical Proofs

Not statistical confidence, but mathematical certainty. Weekend payments are provably impossible.

Edge Case Discovery

Found subtle date collision scenario. Traditional testing would likely have missed this entirely.

Regulatory Excellence

Show auditors formal proofs instead of test results. Gold standard for compliance.

Verify your financial calculations with mathematical certainty

Use CodeLogician to ensure your swap schedulers, pricing engines, and risk calculations are provably correct.

Try CodeLogician

What's at Stake

Company Pays (Fixed Leg)

Bank Pays (Floating Leg)

Business Day Convention

Business Day Adjustment Logic

Python Implementation

Example: Normal Operation

Three Behavioral Regions

Contract Specification

Fixed Leg Cash Flows

All Dates Verified

🇪🇺EMIR (Europe)

🇺🇸Dodd-Frank (US)

📋ISDA Definitions

❌ Traditional Testing

✅ Formal Verification

Mathematical Certainty

Edge Case Discovery

Regulatory Confidence

Complete Coverage

✅ Date Arithmetic

✅ Business Day Conventions

✅ Day Count Fractions

✅ Fixed Income Products

✅ Derivative Contracts

✅ Regulatory Calculations

Mathematical Proofs

Edge Case Discovery

Regulatory Excellence

Verify your financial calculations with mathematical certainty

🇪🇺
EMIR (Europe)

🇺🇸
Dodd-Frank (US)

📋
ISDA Definitions