Derivatives & Portfolio Risk Desk
Quantitative derivatives analytics, Black-Scholes first and second-order Greeks, implied volatility surfaces, multi-leg options payoff structuring, Markowitz mean-variance portfolio optimization, and Value at Risk (VaR). Engineered for derivatives traders, portfolio managers, and risk quants.
Options Greeks & Volatility Surface Workbench
Closed-form Black-Scholes-Merton (1973) pricing with Merton continuous dividend yield adjustments. Calculates 1st- and 2nd-order Greeks, translates exposures into plain-English dollars and cents, plots the post-1987 structural volatility skew curve, and stress-tests 2D spot vs. vol shock matrices.
• Complete Greeks Engine: Delta, Gamma, Vega, Theta, Rho, Vanna
• Plain-English Executive Translations (x100 Multipliers)
• Interactive SVG Volatility Smile & Equity Skew Surface
• 2D Scenario Shock Matrix (35 Joint Spot vs. Vol Scenarios)
• Live Benchmark Risk-Free Rate Hydration (/data/macro_rates.json)
Multi-Leg Options Strategy Payoff & P&L Visualizer
Interactive multi-leg options structuring and payoff engine. Model multi-tranche option spreads, Iron Condors, Straddles, Butterflies, and Collars. Visualize real-time expiration vs. Black-Scholes interim T-t payoff curves, net portfolio Greeks, and Probability of Profit (POP).
• 10 Built-In Institutional Presets (Iron Condor, Long Straddle, Bull Call, Collar, etc.)
• Expiration Intrinsic Payoff vs. Black-Scholes Interim T-t Curve
• Net Strategy Greeks: Delta, Gamma, Vega, Theta, and Break-Even Points
• Probability of Profit (POP) & Max Risk/Reward HUD
Markowitz Efficient Frontier & Portfolio Risk Optimizer
Modern Portfolio Theory (MPT) mean-variance multi-asset allocator. Solves the constrained quadratic optimization problem, plots the real-time Efficient Frontier hyperbola, identifies the Global Minimum Variance (GMVP) and Tangency portfolios, and calculates downside Value-at-Risk (VaR/CVaR).
• Interactive Sliders & Presets (All Weather, 60/40, Endowment)
• Interactive SVG Efficient Frontier & Capital Allocation Line (CAL)
• Tangency (Max Sharpe) & Global Minimum Variance Portfolio Solvers
• Downside Risk: 95% & 99% Parametric VaR & Expected Shortfall (CVaR)
• The \"Free Lunch of Diversification\" Executive Telemetry HUD
Value-at-Risk (VaR) & Expected Shortfall (CVaR) Workbench
Institutional downside tail-risk modeling engine. Calculates Parametric (Normal & Student-t), Historical Simulation, and Monte Carlo (5,000 Cholesky paths) VaR and coherent Expected Shortfall (CVaR) with Basel III traffic-light backtesting.
• Coherent Expected Shortfall (CVaR / Tail Loss Beyond VaR Cutoff)
• Basel III Regulatory Backtesting HUD (Green / Yellow / Red Zones)
• Historical Macro Crisis Shock Replays (2008 GFC, 2020 Covid, 2022 Rates)
• Dynamic SVG Gaussian & Leptokurtic Return Distribution Visualizer
Systematic Volatility Targeting & Risk Parity Allocator
Ray Dalio All-Weather portfolio engine. Decompose marginal risk contributions, solve Equal Risk Contribution (ERC) numerical optimization, eliminate the 60/40 equity risk illusion, and scale leverage dynamically across volatility regimes.
• Nominal Capital Weight vs. True Risk Contribution (RC_i) Comparative HUD
• Systematic Volatility Targeting: Dynamic Gearing via Treasury & Commodity Futures
• Macroeconomic Regime Sensitivity: 4-Quadrant Inflation/Growth Shock Matrix
• Dynamic SVG Volatility Spike & De-leveraging Circuit Breaker Simulator
Derivatives & Portfolio Risk Desk Quantitative Architecture & Methodology
The Derivatives & Portfolio Risk Desk implements closed-form solutions and numerical methods for options pricing and portfolio construction. Models calculate continuous Delta, Gamma, Theta, Vega, and Rho sensitivities alongside matrix-based covariance optimization.
Core Mathematical Formulations
The continuous-time partial differential equation solution determining the theoretical no-arbitrage fair value of European-style options.
First and second-order price sensitivities quantifying directional exposure and the curvature rate of change in hedge ratios.
Solves for the efficient frontier: the set of portfolio asset weights that minimizes total variance for any target expected return.
Quantifies tail-risk threshold losses and the expected severity of extreme portfolio losses beyond the confidence interval cutoff.
Target Institutional Audience & Applications
Options traders managing inventory Greeks, hedging dynamic Gamma and Vega risks, and analyzing volatility skew surfaces.
Asset managers building Markowitz optimal allocations, targeting systematic portfolio volatility, and executing risk parity strategies.
Risk desks stress-testing Value at Risk (VaR) and Conditional VaR under historical volatility shocks.
Cross-Asset Concept Guides & Recommended Reading
Mathematical derivations of Delta, Gamma, Theta, Vega, Vanna, and Volga.
Implied volatility smiles, skew dynamics, and market microstructure supply/demand.
Parametric, historical, and Monte Carlo VaR models with Kupiec backtesting.