Vibeship-spawner-skills derivatives-pricing

id: derivatives-pricing name: Derivatives Pricing category: finance description: Use when pricing options, calculating Greeks, implementing exotic derivatives, or building pricing engines - covers Black-Scholes, binomial trees, Monte Carlo, and QuantLib integration

patterns: golden_rules: - rule: "Calibrate to market" reason: "Model parameters from liquid options" - rule: "Hedge, don't speculate on models" reason: "Greeks show exposure, not truth" - rule: "Check put-call parity" reason: "Arbitrage check for consistency" - rule: "Use implied vol, not historical" reason: "Market prices embed forward-looking info" - rule: "Validate Greeks numerically" reason: "Analytical Greeks can have errors"

method_selection: european_vanilla: "Black-Scholes (Analytical)" american_vanilla: "Binomial/Trinomial Trees" barrier_asian: "Monte Carlo + Variance Reduction" exotic_path_dependent: "Monte Carlo or PDE Methods" volatility_smile: "Heston or Local Vol Models"

black_scholes_formula: | d1 = (ln(S/K) + (r - q + 0.5σ²)T) / (σsqrt(T)) d2 = d1 - σsqrt(T) Call = S*e^(-qT)N(d1) - Ke^(-rT)N(d2) Put = Ke^(-rT)N(-d2) - Se^(-qT)*N(-d1)

greeks: delta: "Price sensitivity to spot" gamma: "Delta sensitivity to spot" theta: "Time decay (daily P&L)" vega: "Sensitivity to volatility" rho: "Sensitivity to rates" vanna: "Delta sensitivity to vol" volga: "Vega sensitivity to vol"

binomial_parameters: | u = exp(σ*sqrt(dt)) # Up factor d = 1/u # Down factor p = (exp((r-q)*dt) - d) / (u - d) # Risk-neutral probability

monte_carlo_exotics: asian: "Average price options with control variate" barrier: "Brownian bridge for barrier crossing" lookback: "Maximum/minimum over path" basket: "Correlated asset simulation"

anti_patterns:

• pattern: "Using historical vol" problem: "Ignores market expectations" solution: "Calibrate to implied vol"
• pattern: "Ignoring dividends" problem: "Misprices options near ex-dates" solution: "Use dividend yield or discrete dividends"
• pattern: "Single model" problem: "Misses skew/smile" solution: "Compare multiple models"
• pattern: "Analytical Greeks only" problem: "Can have errors in exotics" solution: "Verify with bump-and-reprice"
• pattern: "Ignoring early exercise" problem: "Underprices American options" solution: "Use trees or LSM"

implementation_checklist: pricing: - "Choose appropriate model for option type" - "Calibrate to market implied volatility" - "Verify put-call parity holds" - "Handle dividends appropriately" greeks: - "Calculate all relevant Greeks" - "Validate Greeks numerically (bump and reprice)" - "Consider cross-Greeks for complex positions" exotic_options: - "Use variance reduction for Monte Carlo" - "Implement Brownian bridge for barriers" - "Control variate for Asian options" production: - "Backtest hedging performance" - "Document model limitations" - "Set up monitoring for pricing discrepancies"

handoffs:

• skill: risk-modeling trigger: "portfolio VaR with options"
• skill: algorithmic-trading trigger: "options execution strategies"
• skill: portfolio-optimization trigger: "options in portfolio construction"

ecosystem: pricing: - "QuantLib - Full derivatives library" - "py_vollib - Black-Scholes and Greeks" - "mibian - Options pricing" data: - "yfinance - Options chains" - "CBOE - Volatility indices" volatility: - "arch - GARCH modeling" - "volsurface - Vol surface fitting"

sources: tutorials: - "QuantLib Python Bindings 2025" - "The Greeks Explained - Bookdown" books: - "Options, Futures, and Other Derivatives - Hull" - "Volatility Surface - Gatheral"