This project focuses on the intricate task of calibrating the Hull-White model to at-the-money (ATM) caplet market implied volatilities. Through a meticulous process that involves both theoretical and simulation-based approaches, we aim to bridge the gap between model predictions and market observations. Our endeavor is not just an academic exercise but a deep dive into the dynamics of fixed income derivatives, exploring the nuances of the Hull-White model and its practical applications in today's financial markets.
The primary objectives of this project are as follows:
- Data Acquisition: Securely download ATM cap data that serves as the foundation for our calibration process.
- Model Implementation: Develop a theoretical closed-form pricing function specific to the Hull-White model.
- Simulation Verification: Create a Monte-Carlo simulation-based function to verify the consistency of cap pricing with the closed-form solution.
- Model Calibration: Calibrate the Hull-White model to the ATM caplet market data by minimizing the sum of squared pricing errors across model parameters.
The project is structured around a series of MATLAB functions, each tailored to accomplish specific tasks within the model calibration process:
- Black Cap Pricing: Conversion of Bloomberg Market Implied Vol into Dollar Price.
- HW Model Implementation: Including Caplets pricing based on Zero-Bond (ZB) put Pricing, Cap price aggregation from Caplets, analytical solutions and Monte Carlo simulations for ZB and ZB put pricing.
- Optimization Framework: A specialized function designed to optimize the Hull-White model parameters by comparing model-generated cap prices with market prices.
The culmination of this project will be a comprehensive package comprising:
- Source Code: Clean, bug-free, and well-commented MATLAB source code embodying the project's analytical and simulation frameworks.
- Executive Summary: A concise yet detailed report summarizing the project's motivation, implementation strategy, results, and analysis. This report will include tables and graphs comparing model-generated volatilities with market-implied volatilities, alongside a critical discussion on model limitations and fit quality.
The project is segmented into stages, each with specific functions and due dates:
- Stage 1: Implementation of initial pricing and conversion functions, due by April 1.
- Stage 2: Development of cap pricing, analytical solutions, and Monte Carlo simulations for ZB and ZB puts, due by April 8.
- Stage 3: Calibration and optimization of the Hull-White model to market data, due by April 15.
Final submissions are due by April 22, at midnight.
This project is designed as a collaborative exercise, encouraging creativity and intelligent problem-solving. Participants are urged to make justified modeling assumptions, clearly documenting their rationale to foster a robust and transparent calibration process.
The executive report is restricted to 15 pages, focusing exclusively on discussions and graphical analyses. It is expected to be a professional, insightful document that refrains from including source code.
By undertaking this project, we aim to not only enhance our understanding of the Hull-White model and its applications but also contribute to the broader field of fixed income derivatives analysis. This project offers a unique blend of theoretical finance and practical application, challenging participants to apply their knowledge creatively and effectively.