Options Skills

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.

Skill summary

Skill ID	Tool name	Source	Runtime	Description
`options.greeks`	`options_greeks`	computed	interactive	Black-Scholes price + delta/gamma/vega/theta/rho
`options.implied_vol`	`options_implied_vol`	computed	interactive	BS implied vol from observed option price

options.greeks

Black-Scholes option price and full greek set. Arguments

Name	Type	Required	Default	Description
`S`	float	yes	—	Spot price
`K`	float	yes	—	Strike price
`T`	float	yes	—	Time to expiry in years (e.g. `0.25` for 3 months)
`sigma`	float	yes	—	Implied volatility (decimal, e.g. `0.30`)
`r`	float	no	`0.04`	Risk-free rate (decimal)
`q`	float	no	`0.0`	Continuous dividend yield (decimal)
`type`	string	no	`call`	`call` or `put`

Formulas

Output	Formula
`d1`	`(ln(S/K) + (r − q + σ²/2)T) / (σ√T)`
`d2`	`d1 − σ√T`
`call_price`	`S·e^(−qT)·N(d1) − K·e^(−rT)·N(d2)`
`put_price`	`K·e^(−rT)·N(−d2) − S·e^(−qT)·N(−d1)`
`delta`	call: `e^(−qT)·N(d1)`; put: `−e^(−qT)·N(−d1)`
`gamma`	`e^(−qT)·φ(d1) / (S·σ·√T)`
`vega`	`S·e^(−qT)·φ(d1)·√T` (per 1.00 vol)
`theta`	call: `(−S·e^(−qT)·φ(d1)·σ/(2√T) − r·K·e^(−rT)·N(d2) + q·S·e^(−qT)·N(d1)) / 365`
`rho`	call: `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.

options.implied_vol

Black-Scholes implied volatility backed out from an observed option price. Uses Brent’s method on the BS pricing function. Arguments

Name	Type	Required	Default	Description
`S`	float	yes	—	Spot price
`K`	float	yes	—	Strike price
`T`	float	yes	—	Time to expiry in years
`price`	float	yes	—	Observed option price
`r`	float	no	`0.04`	Risk-free rate
`q`	float	no	`0.0`	Continuous dividend yield
`type`	string	no	`call`	`call` or `put`
`tol`	float	no	`1e-6`	Solver tolerance
`max_iter`	int	no	`100`	Max 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.

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.

​Skill summary

​options.greeks

​options.implied_vol

​Next steps

Volatility Skills

Computed Analytics Skills

Skill summary

options.greeks

options.implied_vol

Next steps