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A collection of quantitative finance projects exploring derivatives pricing, risk management, and trading strategies. Combines mathematical theory with practical implementations in Python.

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Quantitative Finance: Theory and Applications

A collection of quantitative finance projects exploring derivatives pricing, risk management, and trading strategies. Combines mathematical theory with practical implementations in Python.

Author: Liam O'Shaughnessy
Background: Princeton Physics (Senior) | HEP Research at CERN
Contact: email | LinkedIn


Theoretical Foundation

I've compiled comprehensive notes covering the mathematical foundations of quantitative finance:

  • Stochastic calculus and martingale theory
  • Derivatives pricing (Black-Scholes, exotic options)
  • Interest rate and credit models
  • Portfolio optimization and risk management
  • Numerical methods (Monte Carlo, finite difference)
  • Machine learning applications

These notes synthesize material from Shreve, Bjork, and academic papers.


Projects

Objective: Model implied volatility dynamics using local and stochastic volatility frameworks.

Key Techniques:

  • Implied volatility surface extraction from SPY options
  • SVI/SSVI parametrization with arbitrage detection
  • Dupire local volatility implementation
  • Heston stochastic volatility calibration (Carr-Madan FFT and Lewis methods)
  • Volatility risk premium estimation

Results: Identified and corrected arbitrage violations in raw SVI, calibrated Heston, estimated vol risk premium.

Tech Stack: Python, NumPy, SciPy, Plotly, yfinance

View Project →


Analysis of implied volatility around earnings announcements and mispricing identification.


Simulation of delta-gamma hedging with transaction costs and comparison to theoretical costs.


Tech Stack

  • Languages: Python, C++ (for performance-critical components)
  • Libraries: NumPy, SciPy, Pandas, Matplotlib/Plotly
  • Data: Yahoo Finance, CBOE, Quandl
  • Tools: Jupyter, Git, VS Code

Background

I'm a Princeton physics senior with research experience in high-energy experimental physics at CERN, focusing on machine learning applications for particle detection and classification. I became interested in quantitative finance while exploring applications of stochastic processes and statistical methods to financial markets.

These projects represent my self-directed learning in mathematical finance, combining rigorous theory with practical implementation.


Contact

Interested in collaborating or have feedback? Reach out:


References

Key resources used in developing these projects:

  • Shreve, S. (2004). Stochastic Calculus for Finance II
  • Bjork, T. (2009). Arbitrage Theory in Continuous Time
  • Koralov and Sinai (1992). Theory of Probability and Random Processes
  • Schilling and Partzsch (2010). Brownian Motion
  • Gatheral, J. (2006). The Volatility Surface
  • Taleb, N. (1997). Dynamic Hedging

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A collection of quantitative finance projects exploring derivatives pricing, risk management, and trading strategies. Combines mathematical theory with practical implementations in Python.

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