Basket Option Pricing Engine

Advanced C# pricing engine for multi-asset derivative products

Master 2 Financial Engineering - Université Paris-Dauphine PSL
Rémi Schmitt & Théo Verdelhan - January 2026

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Overview

Professional-grade basket option pricer implementing both analytical approximations and Monte Carlo simulation with real market data integration (ECB €STR rates, Bloomberg volatility surfaces).

Core Technologies

C# / .NET 9.0 | Quantitative Finance | Numerical Methods | Object-Oriented Design

Key Features

✓ Moment Matching Pricer - Fast analytical approximation (Brigo et al. method)
✓ Monte Carlo Engine - Reference pricing with 98.6% variance reduction via control variates
✓ Dual Framework - H1 (constant parameters) and H2 (term structure modeling)
✓ Real Market Data - ECB €STR rates and Bloomberg OVDV volatility surfaces
✓ Production-Ready - 15 automated tests validating mathematical and economic properties

Performance

Method	Speed	Accuracy
Moment Matching	< 1ms	Excellent for standard cases
Monte Carlo (1M sims)	~500ms	Reference-grade with variance reduction

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Technical Implementation

Architecture

Clean object-oriented design following quantitative finance best practices:

BasketOptionPricer/
├── Models/           Stock, Basket, BasketOption, Term structures
├── Pricers/          MomentMatching (H1/H2), MonteCarlo
├── Utils/            Mathematical functions (Normal CDF, Black-Scholes)
├── Data/             Market data loaders (CSV parsing)
└── Tests/            Unit tests (7) + Functional tests (8)

Mathematical Models

H1 Framework - Black-Scholes with constant parameters:

• Geometric Brownian motion: dSᵢ = (r-qᵢ)Sᵢdt + σᵢSᵢdWᵢ
• Analytical moment matching for fast pricing
• Full correlation matrix support

H2 Framework - Deterministic term structures:

• Time-varying rates: r(t) and volatilities: σᵢ(t)
• Numerical integration via trapezoidal rule
• Linear interpolation between term points

Monte Carlo Engine:

• Cholesky decomposition for correlated paths
• Log-Euler discretization scheme (252+ steps/year)
• Control variate variance reduction (geometric mean basket)

Key Algorithms Implemented

1. Cholesky Decomposition - O(n³) correlation matrix factorization
2. Trapezoidal Integration - Numerical term structure integration
3. Normal CDF - Abramowitz & Stegun approximation (|error| < 1.5×10⁻⁷)
4. Moment Matching - Lognormal basket approximation calibrated to first two moments

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Results & Validation

Numerical Accuracy

H1 Pricing Example (3-asset basket, 1Y maturity, €STR 1.933%):

• Call option (K=107.10€): 4.89€
• Put option (K=96.90€): 3.75€

H2→H1 Convergence: Perfect match (0.0000% error) when term structures are flat

Monte Carlo Variance Reduction:

Standard MC:        SE = 0.0568  
With Control Var:   SE = 0.0066  →  98.6% variance reduction

Comprehensive Testing

Unit Tests (7):

• Mathematical functions (Normal CDF, Black-Scholes)
• Object construction and validation
• Strike monotonicity and boundary conditions

Functional Tests (8):

• Multi-asset basket configurations
• Framework convergence validation
• Correlation sensitivity analysis
• Put-call relationship consistency

All tests include tolerance checks and economic property validation.

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Usage

Quick Start

dotnet build -c Release
dotnet run -c Release

Interactive Interface

User-friendly menu system for:

1. Auto Demo - Pre-configured H1/H2 comparison scenarios
2. Interactive Mode - Custom basket configuration wizard
3. Test Suite - Automated validation (unit + functional)
4. Bloomberg Data - Volatility surface analysis

Example: Custom Pricing

🎯 Configure basket (2-10 assets)
💰 Input market parameters (rates, correlations, volatilities)
📋 Define option (Call/Put, Strike, Maturity)
⚡ Price with Moment Matching or Monte Carlo
📊 Get results with confidence intervals

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Market Data Integration

Risk-Free Rate: €STR (Euro Short-Term Rate) from ECB

• Real historical data: Oct 2019 - Jan 2026
• Current rate: 1.933% (Jan 23, 2026)

Volatility Surfaces: Bloomberg OVDV for Euro Stoxx 50

• Multiple maturities and moneyness points
• Linear interpolation for continuous surface

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Technical Skills Demonstrated

Programming: C# 9.0, .NET SDK, OOP design patterns, LINQ

Finance: Derivative pricing, Black-Scholes model, Monte Carlo methods, variance reduction techniques, term structure modeling

Mathematics: Stochastic calculus, numerical integration, matrix decomposition, statistical estimation

Software Engineering: Unit testing, functional testing, input validation, error handling, clean code architecture

Data: CSV parsing, real market data integration (ECB, Bloomberg)

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References

Academic: Brigo et al. (2004) - Moment matching for basket options | Glasserman (2003) - Monte Carlo methods in finance

Data Sources: European Central Bank (€STR rates) | Bloomberg Terminal (OVDV surfaces)

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Quick Reference

# Build optimized version
dotnet build -c Release

# Run application
dotnet run -c Release

# Test suite
dotnet run → Option 3 (Unit) / Option 4 (Functional)

Project Structure: 1000+ lines of C# across Models, Pricers, Utils, Tests
Test Coverage: 15 automated tests (100% pass rate)
Performance: Release mode 2-3× faster than Debug

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M2 Quantitative Finance Project - Université Paris-Dauphine PSL
Full technical documentation available in ReproductionParameters.md