workflow-derivatives-option-pricing

# Option Pricing Workflow ## What this skill covers A structured pipeline for pricing vanilla options (European and American), extracting a complete Greeks profile, and validating the implied-volatility input against historical realized volatility. Every number in the output must originate from a tool call; no hand-calculation is permitted. Covers equity, index, FX, and commodity underlyings. ## Workflow ### Phase 1 — Market Data Ingestion 1. **Spot price**: call `fmp_quote` with the underlying symbol to obtain the current mid price. 2. **Risk-free rate**: call `fmp_treasury_rates` for the US Treasury yield matching the option tenor, or `fred_yield_curve` for the SOFR/LIBOR-equivalent curve. 3. **Dividend yield / carry cost**: retrieve from `fmp_key_metrics` (trailing dividend yield) or `fmp_financial_ratios` for equity underlyings. For FX underlyings use the foreign interest rate sourced from `fred_series`. 4. **Observed market price** (if MTM mode): pull `yf_options_chain` for the specific expiry and strike to obtain the market mid price and existing market-derived Greeks. ### Phase 2 — Implied Volatility Extraction 5. When a market option price is available, call `implied_volatility` with the market price, spot, strike, rate, tenor, and dividend yield. - Flag any result where IV < 2% or IV > 150% as suspect; request an alternative market price before continuing. - For American options, specify the binomial-tree solver to account for early exercise. ### Phase 3 — Historical Volatility Cross-Check 6. Call `fmp_historical_price` for the underlying with a look-back window matching the option tenor (e.g., 30-day option → 30 days of daily closes). 7. Compute realized volatility annualized as `sqrt(252) * std(log returns)`. Pass the raw close series to `monte_carlo_simulation` with distributional mode set to normal to obtain the annualized vol estimate independently. 8. Compare IV from Phase 2 against historical realized vol: - IV / HV > 1.3: premium selling bias; flag. - IV / HV < 0.7: cheap vol; flag. - Document the IV-HV spread in the output table. ### Phase 4 — Option Pricing 9. Call `option_pricer` with the following parameters: - `model`: `"black_scholes"` for European; `"binomial"` for American, barrier, or dividend-paying underlyings with discrete dividends. - `spot`, `strike`, `rate`, `tenor`, `volatility` (use IV from Phase 2 if available; else use HV or analyst assumption). - `dividend_yield` or `cost_of_carry` as applicable. - `option_type`: `"call"` or `"put"`. - `steps` (binomial only): minimum 200 for American options. 10. Extract from the tool response: `price`, `delta`, `gamma`, `theta`, `vega`, `rho`. 11. Run put-call parity cross-check: `C - P = S * exp(-q*T) - K * exp(-r*T)`. Any discrepancy > $0.01 for liquid underlyings must be investigated. ### Phase 5 — Intrinsic vs Time Value Decomposition 12. Compute: - **Intrinsic value**: `max(S - K, 0)` for calls; `max(K - S, 0)` for puts. - **Time value**: `option price - intrinsic value`. - State whether the option is ITM, ATM, or OTM and quantify the moneyness ratio `S/K`. ### Phase 6 — Scenario Sensitivity 13. Call `sensitivity_matrix` with spot ± 10% / ± 20% on one axis and implied vol ± 5 vol points on the other axis to produce a 5 × 5 price grid. ## Output Format ### Option Pricing Summary | Parameter | Value | Source | |---|---|---| | Underlying | — | `fmp_quote` | | Spot price | — | `fmp_quote` | | Strike | — | Input | | Expiry (days) | — | Input | | Risk-free rate | — | `fmp_treasury_rates` | | Dividend yield | — | `fmp_key_metrics` | | Implied volatility | — | `implied_volatility` | | Historical vol (HV) | — | `fmp_historical_price` | | IV / HV ratio | — | Computed | | **Option fair value** | — | `option_pricer` | | Intrinsic value | — | Computed | | Time value | — | Computed | ### Greeks Table | Greek | Value | Interpretation | |---|---|---| | Delta | — | $ change per $1 spot move | | Gamma | — | Delta change per $1 spot move | | Theta | — | $ decay per calendar day | | Vega | — | $ change per 1 vol point | | Rho | — | $ change per 1% rate move | ### Sensitivity Matrix: Price vs Spot and Vol (5 × 5 grid — output from `sensitivity_matrix`) ### Tool-Call Traceability | # | Tool | Key Inputs | Output | |---|---|---|---| ## Quality Gates - [ ] Spot price sourced from `fmp_quote` or equivalent live data; not hard-coded. - [ ] Risk-free rate tenor matches option expiry within 30 days. - [ ] IV extracted by `implied_volatility` tool call; never hand-estimated. - [ ] HV cross-check performed; IV/HV ratio documented. - [ ] Put-call parity verified: discrepancy ≤ $0.01 for liquid underlyings. - [ ] American-exercise options priced with binomial (`steps` ≥ 200), not Black-Scholes. - [ ] Greeks sign conventions confirmed: long call — delta > 0, gamma > 0, theta < 0, vega > 0. - [ ] Sensitivity matrix (`sensitivity_matrix`) produced for every deliverable. - [ ] Every number in output maps to a row in the traceability table. ## Related Skills - `workflow-derivatives-vol-surface` — construct a full IV surface; inputs feed this skill's Phase 2. - `workflow-derivatives-option-strategies` — aggregate Greeks across multi-leg structures. - `workflow-derivatives-structured-products` — vanilla option pricing as component of structured notes. - `corp-finance-analyst-derivatives` — agent body with full tool inventory and calling conventions.