Production-ready Swift library for financial analysis, forecasting, and quantitative modeling.
Build DCF models, optimize portfolios, run Monte Carlo simulations, and value securities—with industry-standard implementations (ISDA, Black-Scholes) that work out of the box.
Major milestone: Production-ready API with role-based financial statements, GPU-accelerated optimization, multiple linear regression, and comprehensive operator tools.
- ✅ Role-Based Financial Statements: Multi-statement account support for accurate financial modeling
- ✅ GPU Acceleration: 10-100× speedup for genetic algorithms (populations ≥ 1,000) on Apple Silicon
- ✅ Consistent API:
initialGuessparameter everywhere,@Sendableclosures for Swift 6 concurrency - ✅ Constraint Support: Equality and inequality constraints via penalty method
- ✅ Multiple Linear Regression: GPU-accelerated matrix backends (CPU / Accelerate / Metal) for statistical modeling
- ✅ Operator Helpers: Contribution margin, debt classification, pro forma adjustments, working capital tracking
- ✅ 100% Documentation Coverage: All public APIs fully documented
- ✅ 4,558+ Tests: All passing with strict concurrency compliance
Current Status: v2.0.0 - Production-ready release
See what's new: CHANGELOG.md
Type-Safe & Concurrent: Full Swift 6 compliance with generics (TimeSeries<T: Real>) and strict concurrency for thread safety. All examples include @Sendable closures and proper PlaygroundSupport integration.
Complete: 61 comprehensive guides, 4,558+ tests, and production implementations of valuation models, optimization algorithms, and risk analytics. Every tutorial example has been validated to work correctly in Xcode Playgrounds and production code.
Accurate: Calendar-aware calculations (365.25 days/year), industry-standard formulas (ISDA CDS pricing, Black-Scholes), and validated against real-world use cases. Documentation examples reflect actual API behavior with realistic tradeoffs (mean-variance optimization, risk constraints, budget limits).
Fast: Sub-millisecond NPV/IRR calculations, complete forecasts in <50ms, optimized for interactive dashboards and real-time analysis.
Ergonomic: Fluent APIs that read like financial prose. Risk-aware examples that demonstrate real tradeoffs, not trivial solutions. Clear error messages and comprehensive debugging guides.
import BusinessMath
// Complete investment analysis workflow
let cashFlows = [-100_000.0, 30_000, 40_000, 50_000, 60_000]
// 1. Evaluate profitability
let npvValue = npv(discountRate: 0.10, cashFlows: cashFlows)
// → $38,877 ✓ Positive NPV
let irrValue = try irr(cashFlows: cashFlows)
// → 24.9% return ✓ Exceeds hurdle rate
let pi = profitabilityIndex(rate: 0.10, cashFlows: cashFlows)
// → 1.389 ✓ Good investment (> 1.0)
// 2. Sensitivity analysis: How sensitive is NPV to discount rate?
let rates = [0.05, 0.07, 0.10, 0.12, 0.15]
let sensitivityTable = DataTable<Double, Double>.oneVariable(
inputs: rates,
calculate: { rate in npv(discountRate: rate, cashFlows: cashFlows) }
)
for (rate, npvResult) in sensitivityTable {
print("Rate: \((rate * 100).smartRounded())%: NPV: \(npvResult.currency())")
}
// Shows NPV ranges from $57K (5% rate) to $23K (15% rate)
// 3. Risk assessment: Monte Carlo simulation for uncertain cash flows
var simulation = MonteCarloSimulation(iterations: 10_000) { inputs in
// Model uncertain cash flows with ±20% volatility
let year1 = 30_000 * (1 + inputs[0])
let year2 = 40_000 * (1 + inputs[1])
let year3 = 50_000 * (1 + inputs[2])
let year4 = 60_000 * (1 + inputs[3])
return npv(discountRate: 0.10, cashFlows: [-100_000, year1, year2, year3, year4])
}
// Add uncertainty inputs (normal distribution with 20% std dev)
for year in 1...4 {
simulation.addInput(SimulationInput(
name: "Year \(year) Return Variance",
distribution: DistributionNormal(0.0, 0.20)
))
}
let results = try simulation.run()
let var95 = results.valueAtRisk(confidenceLevel: 0.95)
print("\nRisk Analysis:")
print("Expected NPV: \(results.statistics.mean.currency())")
print("95% VaR: \(abs(var95).currency()) (worst case with 95% confidence)")
print("Probability of loss: \((results.probabilityBelow(0) * 100).number())%")
// → Decision: Approve investment ✓
// Strong positive NPV, profitable across rate scenarios, low probability of lossThis shows the power of BusinessMath: calculate, analyze, and decide in one workflow.
Build revenue models, forecast cash flows, and model business scenarios with calendar-aware time series operations. Supports daily through annual periods with fiscal calendar alignment (Apple, Australia, UK, etc.).
→ Guide: Building Revenue Models | Forecasting Guide
Calculate NPV, IRR, MIRR, profitability index, and payback periods. Handle irregular cash flows with XNPV/XIRR. Includes loan amortization with payment breakdowns (PPMT, IPMT).
→ Guide: Investment Analysis | Time Value of Money
Value equities (DCF, DDM, FCFE, residual income), price bonds (duration, convexity, credit spreads), and analyze credit derivatives (CDS pricing with ISDA Standard Model, Merton structural model).
→ Equity Valuation | Bond Valuation | Credit Derivatives
Run Monte Carlo simulations with 15 probability distributions. Calculate VaR/CVaR, perform stress testing, and aggregate portfolio risks. Model uncertainty with scenario analysis.
→ Monte Carlo Guide | Risk Analytics
Optimize portfolios (efficient frontier, Sharpe ratio maximization), solve integer programming problems (branch-and-bound, cutting planes), and allocate capital optimally. GPU-accelerated genetic algorithms provide 10-100× speedup for large-scale optimization (populations ≥ 1,000) with automatic Metal acceleration on Apple Silicon.
→ Portfolio Optimization | Optimization Guide | GPU Acceleration
Add BusinessMath to your Package.swift:
dependencies: [
.package(url: "https://github.com/jpurnell/BusinessMath.git", from: "2.0.0")
]Or in Xcode: File → Add Package Dependencies → Enter repository URL
61 comprehensive guides organized into 5 parts (Basics, Analysis, Modeling, Simulation, Optimization):
- Documentation Home - Complete structure and index
- Learning Path Guide - Four specialized tracks:
- Financial Analyst (15-20 hours)
- Risk Manager (12-15 hours)
- Quantitative Developer (20-25 hours)
- General Business (10-12 hours)
- Getting Started - Quick introduction with examples
Detailed examples for common workflows:
- QUICK_START_EXAMPLE.swift - 🚀 Copy-paste investment analysis example (start here!)
- EXAMPLES.md - Time series, forecasting, loans, securities, risk, optimization
- All DocC Tutorials - 61 comprehensive guides with runnable examples
- ✅ Generic time series with calendar-aware operations
- ✅ Time value of money (NPV, IRR, MIRR, XNPV, XIRR, annuities)
- ✅ Forecasting (trend models: linear, exponential, logistic)
- ✅ Seasonal decomposition (additive and multiplicative)
- ✅ Growth modeling (CAGR, trend fitting)
- ✅ Loan amortization (payment schedules, PPMT, IPMT)
- ✅ Financial statements (role-based architecture with multi-statement account support)
- ✅ Securities valuation (equity: DCF, DDM, FCFE; bonds: pricing, duration, convexity; credit: CDS, Merton model)
- ✅ Risk analytics (VaR, CVaR, stress testing)
- ✅ Monte Carlo simulation (15 distributions, sensitivity analysis)
- ✅ Portfolio optimization (efficient frontier, Sharpe ratio, risk parity)
- ✅ Genetic algorithms (GPU-accelerated for populations ≥ 1,000, automatic Metal acceleration)
- ✅ Integer programming (branch-and-bound, cutting planes)
- ✅ Financial ratios (profitability, leverage, efficiency)
- ✅ Real options (Black-Scholes, binomial trees, Greeks)
- ✅ Multiple linear regression (OLS with QR decomposition; CPU, Accelerate, and Metal matrix backends)
- ✅ Hypothesis testing (t-tests, chi-square, F-tests, A/B testing)
- ✅ Model validation (fake-data simulation, parameter recovery)
- 📚 61 comprehensive guides (48,000+ lines of DocC documentation)
- ✅ 4,558+ tests across 285+ test suites (100% pass rate)
- 📊 Performance benchmarks for typical use cases
- 🎓 Learning paths for different roles
- Swift 6.0 or later
- Platforms: iOS 14+ / macOS 13+ / tvOS 14+ / watchOS 7+ / visionOS 1+ / Linux
- Dependencies: Swift Numerics (for
Realprotocol)
- Financial Analysts: Revenue forecasting, DCF valuation, scenario analysis
- Risk Managers: VaR/CVaR calculation, Monte Carlo simulation, stress testing
- Corporate Finance: Capital allocation, WACC, financing decisions, lease accounting
- Portfolio Managers: Efficient frontier, Sharpe ratio optimization, risk parity
- Quantitative Developers: Algorithm implementation, model validation, backtesting
- FP&A Teams: Budget planning, KPI tracking, executive dashboards
📢 v2.0.0 Release Notes - Complete what's new guide for the 2.0 release
Contributions welcome! Please:
- Fork the repository
- Create a feature branch (
git checkout -b feature/amazing-feature) - Ensure all tests pass (
swift test) - Add tests for new functionality
- Update documentation
- Open a Pull Request
📖 See CONTRIBUTING.md for detailed guidelines and code standards.
MIT License - see LICENSE for details.
- Documentation: BusinessMath.docc
- Issues: GitHub Issues
- Discussions: GitHub Discussions
- Examples: QUICK_START_EXAMPLE.swift | EXAMPLES.md