Stochastic Volatility and the Failure of Black-Scholes: A Practitioner's Guide to Better Pricing
Why constant volatility fails when it matters most, and which stochastic models actually improve hedging performance.
Credit Risk Modeling: From Structural to Reduced Form Approaches
Understanding when default models explain versus calibrate determines whether you're pricing credit risk or just running formulas.
Optimal Execution: Minimizing Market Impact in Large Trades
The mathematical framework for executing institutional trades while minimizing the inescapable trade-off between market impact and timing risk.
Copulas in Risk Management: Modeling Dependence Beyond Correlation
Why correlation fails during crises and how copulas capture the tail dependence that determines portfolio survival
Portfolio Optimization Under Parameter Uncertainty: Escaping the Markowitz Trap
Why the most mathematically elegant portfolio theory produces the worst practical results—and how to fix it
Counterparty Credit Risk: CVA, DVA, and the Pricing of Default Contingency
How bilateral default risk reshapes derivative valuation through sophisticated credit adjustments that have become central to modern dealer operations.
Liquidity Risk Pricing: The Hidden Premium Institutional Investors Miss
Decomposing and harvesting the systematic returns that compensate patient capital for bearing trading frictions others cannot tolerate.
The Term Structure of Interest Rates: Affine Models and Their Trading Implications
Understanding why affine models dominate fixed income analytics and how their mathematical structure informs sophisticated relative value strategies.
The Cross-Section of Expected Returns: Beyond Fama-French
Separating genuine return predictors from statistical mirages in the crowded landscape of factor-based investing strategies
Momentum and Mean Reversion: The Statistical Foundations of Time-Series Predictability
Rigorous statistical frameworks reveal when asset price predictability creates genuine profit opportunities versus statistical mirages.
Machine Learning Factor Selection: Statistical Discipline for the Algorithm Age
Rigorous statistical frameworks transform machine learning from overfitting engine into genuine factor discovery tool for quantitative practitioners.
Why Your Factor Model Is Lying to You: The Hidden Dynamics of Time-Varying Betas
Static betas mask dynamic risk exposures that spike during crises—conditional estimation frameworks reveal what unconditional models hide.
Jump Diffusion Models: Capturing the Fat Tails Markets Actually Exhibit
Why your risk models systematically underestimate market crashes and how jump processes fix the mathematics of extreme events.