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
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)
These notes synthesize material from Shreve, Bjork, and academic papers.
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
Objective: Understand how historical volatility and implied volatility behave with stock behavior around earnings announcements.
Key Techniques:
- Historical Volatility (HV) baseline vs. Event-driven Realized Volatility
- "Earnings multiplier" analysis (
$RV_{earnings} / \sigma_{baseline}$ ) across GICS sectors - VIX regime conditioning
- Directional bias and "Win Rate" statistical testing
- IV analysis (coming soon with better historical data)
Results: Identified that the Communication Services sector exhibit the highest shock multiplier (~4.2x), while Energy displays the lowest (~2.0x). Confirmed that earnings multipliers contract during High-VIX regimes due to volatility normalization.
Tech Stack: Python, Pandas, Matplotlib, Seaborn, yfinance
3. Options Greeks and Dynamic Hedging (Coming Soon)
Simulation of delta-gamma hedging with transaction costs and comparison to theoretical costs.
- Languages: Python, C++ (for performance-critical components)
- Libraries: NumPy, SciPy, Pandas, Matplotlib/Plotly
- Data: Yahoo Finance, CBOE, Quandl
- Tools: Jupyter, Git, VS Code
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.
Interested in collaborating or have feedback? Reach out:
- Email: lo8603@princeton.edu
- LinkedIn: Liam O'Shaughnessy
- GitHub: @liamos7
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