workflow-derivatives-option-pricing

name	workflow-derivatives-option-pricing
description	WHAT: Price European and American options via Black-Scholes and binomial tree; extract full Greeks; cross-check implied volatility against historical realized volatility. WHEN: Invoke for single-leg option pricing, hedging analysis, position mark-to-market, or any task requiring a defensible fair-value estimate with Greeks.

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.

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• corp-finance-analyst-derivatives — agent body with full tool inventory and calling conventions.