Trinomial Option Pricer in C#

Academic Project — M2 272 Quantitative Finance, Université Paris Dauphine-PSL
Théo Verdelhan & Arthur Le Net

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Overview

This repository contains a high-performance trinomial tree pricer for European and American options, implemented in C# and supporting discrete dividends. The code is a faithful translation of a validated Python implementation, with a focus on numerical accuracy, extensibility, and computational efficiency.

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Features

• European & American option pricing (call/put)
• Discrete dividend support (date & amount)
• Fast convergence to Black-Scholes analytical price
• Calculation of Greeks (Delta, Gamma, Theta, Vega, Rho)
• Modular, object-oriented architecture
• Extensive validation and test suite

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Academic Context

This project was developed as part of the M2 272 Quantitative Finance course at Université Paris Dauphine-PSL. The assignment required:

1. Faithful translation of a Python trinomial pricer to C#
2. Numerical validation against Black-Scholes
3. Implementation of dividend handling and Greeks
4. Performance optimization and code structuring

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Installation

Prerequisites

• .NET 9.0 or higher

Quick Start

# Clone the repository
git clone https://github.com/theov07/Trinomial_Option_Pricer_CSharp.git
cd Trinomial_Option_Pricer_CSharp

# Build
dotnet build

# Run
dotnet run

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Usage

All main parameters can be set in Tester/TesterPricer.cs (see the Main() method):

var market = new Market(s0: 100.0, rate: 0.05, sigma: 0.30, dividend: 3.0, 
                       exDivDate: DateTime.Parse("2026-04-21"));

To change the scenario, simply edit the values for:

• s0: Initial underlying price
• rate: Risk-free rate
• sigma: Volatility
• dividend: Dividend amount
• exDivDate: Ex-dividend date

Running Specific Tests

# Convergence test
dotnet run | grep -A 10 "CONVERGENCE"

# Greeks test
dotnet run | grep -A 10 "GREEKS"

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Project Structure

CSharp-Pricer-Verdelhan-LeNet/
├── Core/                    # Main pricer classes
│   ├── Market.cs           # Market parameters
│   ├── Option.cs           # Option definition
│   ├── Node.cs             # Tree node
│   ├── Tree.cs             # Trinomial tree logic
│   ├── BlackScholes.cs     # Analytical Black-Scholes model
│   └── Greeks.cs           # Sensitivities (Greeks)
├── Tester/                 # Test and demo scripts
│   └── TesterPricer.cs     # Main test runner
├── TrinomialPricer.csproj  # .NET project file
└── README.md               # Documentation

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Validation & Performance

• Convergence: Error < 1 cent vs Black-Scholes for 400 steps
• Speed: < 2 seconds for 400 steps (~80,000 nodes)
• Dividend Handling: Correct price adjustment for discrete dividends
• Greeks: Delta, Gamma, Theta, Vega, Rho validated numerically

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References

• Black, F., & Scholes, M. (1973). The Pricing of Options and Corporate Liabilities. Journal of Political Economy, 81(3), 637-654.
• Hull, J. C. (2018). Options, Futures, and Other Derivatives (10th Edition).
• Cox, J. C., Ross, S. A., & Rubinstein, M. (1979). Option Pricing: A Simplified Approach. Journal of Financial Economics, 7(3), 229-263.

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License

This project is for academic purposes. The code is provided as-is for educational use.

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Contact

For questions or feedback:

• Théo Verdelhan — theo.verdelhan@dauphine.eu

Developed at Université Paris Dauphine-PSL