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Options skills are pure computed analytics — they take agent-supplied inputs (no archive reads) and run Black-Scholes math. This makes them deterministic, instant, and free of provenance caveats. The provenance envelope returns source: "computed" with lag_seconds: 0.
Because these skills don’t touch the archive, the agent supplies every input. Use vol.term_structure or market.quote first if you need market IV or spot.

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Skill summary

Skill IDTool nameSourceRuntimeDescription
options.greeksoptions_greekscomputedinteractiveBlack-Scholes price + delta/gamma/vega/theta/rho
options.implied_voloptions_implied_volcomputedinteractiveBS implied vol from observed option price

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options.greeks

Black-Scholes option price and full greek set. Arguments
NameTypeRequiredDefaultDescription
Sfloatyes—Spot price
Kfloatyes—Strike price
Tfloatyes—Time to expiry in years (e.g. 0.25 for 3 months)
sigmafloatyes—Implied volatility (decimal, e.g. 0.30)
rfloatno0.04Risk-free rate (decimal)
qfloatno0.0Continuous dividend yield (decimal)
typestringnocallcall or put
Formulas
OutputFormula
d1(ln(S/K) + (r − q + σ²/2)T) / (σ√T)
d2d1 − σ√T
call_priceS·e^(−qT)·N(d1) − K·e^(−rT)·N(d2)
put_priceK·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1)
deltacall: e^(−qT)·N(d1); put: −e^(−qT)·N(−d1)
gammae^(−qT)·φ(d1) / (S·σ·√T)
vegaS·e^(−qT)·φ(d1)·√T (per 1.00 vol)
thetacall: (−S·e^(−qT)·φ(d1)·σ/(2√T) − r·K·e^(−rT)·N(d2) + q·S·e^(−qT)·N(d1)) / 365
rhocall: K·T·e^(−rT)·N(d2) / 100
Example 
options_greeks({ "S": 128.42, "K": 130, "T": 0.0822, "sigma": 0.42, "r": 0.045, "type": "call" })

{
  "skill_id": "options.greeks",
  "data": {
    "inputs": { "S": 128.42, "K": 130, "T": 0.0822, "sigma": 0.42, "r": 0.045, "q": 0.0, "type": "call" },
    "price": 5.18,
    "greeks": { "delta": 0.521, "gamma": 0.038, "vega": 0.182, "theta": -0.087, "rho": 0.044 },
    "d1": 0.052, "d2": -0.068
  },
  "provenance": { "source": "computed", "freshness": { "as_of": "2025-06-27T20:00:00Z", "lag_seconds": 0 }, "cost": { "credits": 1, "tier": "free" }, "warnings": [] }
}
vega is reported per 1.00 (100%) change in vol. Divide by 100 for per-percentage-point sensitivity. theta is reported per calendar day.

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options.implied_vol

Black-Scholes implied volatility backed out from an observed option price. Uses Brent’s method on the BS pricing function. Arguments
NameTypeRequiredDefaultDescription
Sfloatyes—Spot price
Kfloatyes—Strike price
Tfloatyes—Time to expiry in years
pricefloatyes—Observed option price
rfloatno0.04Risk-free rate
qfloatno0.0Continuous dividend yield
typestringnocallcall or put
tolfloatno1e-6Solver tolerance
max_iterintno100Max iterations
What it computes: finds sigma such that BS(S, K, T, sigma, r, q, type) = price. Example 
options_implied_vol({ "S": 128.42, "K": 130, "T": 0.0822, "price": 5.18, "r": 0.045, "type": "call" })

{
  "skill_id": "options.implied_vol",
  "data": {
    "inputs": { "S": 128.42, "K": 130, "T": 0.0822, "price": 5.18, "r": 0.045, "type": "call" },
    "implied_vol": 0.4201, "iterations": 12, "converged": true
  },
  "provenance": { "source": "computed", "freshness": { "as_of": "2025-06-27T20:00:00Z", "lag_seconds": 0 }, "cost": { "credits": 1, "tier": "free" }, "warnings": [] }
}
If converged is false, the implied vol is an approximation. This usually means the price is below intrinsic (arbitrage violation) or the inputs are inconsistent. Check warnings in the envelope.

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Next steps

Volatility Skills

Realized vol, IV rank, variance risk premium, and regime classification — computed from archive closes.

Computed Analytics Skills

Correlations, factor exposures, DCF, portfolio optimization, Monte Carlo, and tearsheets.