Greeks

Nautilus provides two paths for working with option Greeks (sensitivities of option prices to changes in market variables):

Venue-provided Greeks (Rust/PyO3): real-time Greeks streamed from venues like Deribit, Bybit, and OKX via the OptionGreeks data type and the option chain aggregation system.
Local Greeks calculator (Cython/Python): the GreeksCalculator class that computes Black-Scholes Greeks from cached market data, with support for portfolio aggregation, shock scenarios, and beta weighting.

Either path works independently or together. Venue-provided Greeks arrive through the data subscription system and require no local computation. The local calculator covers venues that do not stream Greeks, backtesting, and custom adjustments (shocks, beta weighting, percent Greeks).

Venue-provided Greeks (Rust/PyO3)

OptionGreeks

The OptionGreeks type represents venue-provided sensitivities for a single option contract. It is a Rust-native type exposed to Python via PyO3.

Field	Type	Description
`instrument_id`	`InstrumentId`	The option contract these Greeks apply to.
`delta`	`float`	Rate of change of option price per unit underlying.
`gamma`	`float`	Rate of change of delta per unit underlying.
`vega`	`float`	Sensitivity to a 1% change in implied volatility.
`theta`	`float`	Daily time decay (dV/dt / 365.25).
`rho`	`float`	Sensitivity to a change in interest rate.
`mark_iv`	`float` or None	Mark implied volatility.
`bid_iv`	`float` or None	Bid implied volatility.
`ask_iv`	`float` or None	Ask implied volatility.
`underlying_price`	`float` or None	Underlying price at time of calculation.
`open_interest`	`float` or None	Open interest for the contract.
`ts_event`	`int`	UNIX timestamp (nanoseconds) of the event.
`ts_init`	`int`	UNIX timestamp (nanoseconds) when initialized.

Subscribe from an actor or strategy:

python

self.subscribe_option_greeks(instrument_id, client_id=ClientId("DERIBIT"))

Handle updates:

python

def on_option_greeks(self, greeks: OptionGreeks) -> None:
    self.log.info(f"delta={greeks.delta:.4f} gamma={greeks.gamma:.6f}")

See the Options guide for the full subscription API including option chain aggregation, strike range filtering, and snapshot modes.

Underlying Rust types

The core Rust implementation lives in crates/model/src/data/greeks.rs:

OptionGreekValues: a plain struct with delta, gamma, vega, theta, rho fields. Implements Add and Mul<f64> for aggregation.
OptionGreeks (in crates/model/src/data/option_chain.rs): wraps OptionGreekValues with instrument_id, implied volatility fields, and timestamps. Implements Deref<Target = OptionGreekValues> so you can access Greeks fields directly.
HasGreeks trait: provides a greeks() method returning OptionGreekValues. Implemented by both OptionGreekValues and OptionGreeks.

Black-Scholes functions (Rust/PyO3)

Low-level pricing functions exposed to Python from crates/model/src/data/greeks.rs:

python

from nautilus_trader.core.nautilus_pyo3 import (
    black_scholes_greeks,
    imply_vol,
    imply_vol_and_greeks,
    refine_vol_and_greeks,
)

# Compute Greeks given known volatility
result = black_scholes_greeks(s=100.0, r=0.05, b=0.0, vol=0.20, is_call=True, k=100.0, t=0.25)
# result.delta, result.gamma, result.vega, result.theta, result.price, result.vol

# Imply volatility from market price, then compute Greeks
result = imply_vol_and_greeks(s=100.0, r=0.05, b=0.0, is_call=True, k=100.0, t=0.25, price=5.0)

# Refine volatility from a starting vol estimate (faster convergence)
result = refine_vol_and_greeks(s=100.0, r=0.05, b=0.0, is_call=True, k=100.0, t=0.25,
                                target_price=5.0, initial_vol=0.18)

The BlackScholesGreeksResult returned by these functions contains: price, vol, delta, gamma, vega, theta, and itm_prob.

Conventions:

Vega is scaled by 0.01 (sensitivity to a 1 percentage point vol change).
Theta is scaled by 1/365.25 (daily decay).
American-style options are priced as European for Greeks computation.

Local Greeks calculator (Cython/Python)

GreeksCalculator

The GreeksCalculator class in nautilus_trader/model/greeks.pyx computes Black-Scholes Greeks from cached market data. It is accessible from any actor or strategy.

python

from nautilus_trader.model.greeks import GreeksCalculator

# Typically created in on_start()
calculator = GreeksCalculator(cache=self.cache, clock=self.clock)

Instrument Greeks

Compute Greeks for a single instrument (option or underlying) with quantity of 1:

python

greeks = calculator.instrument_greeks(
    instrument_id=option_id,
    flat_interest_rate=0.0425,  # used if no yield curve in cache
)
# Returns GreeksData or None

The calculator:

Looks up the instrument and its underlying in the cache.
Retrieves current prices (MID preferred, LAST as fallback).
Looks up yield curves from the cache (falls back to flat_interest_rate).
Implies volatility from the market price using imply_vol_and_greeks.
Returns a GreeksData object with all computed values.

For non-option instruments (futures, equities), the calculator returns a GreeksData with delta=1 (or beta-weighted delta) and no gamma/vega/theta.

Shock scenarios: apply hypothetical changes to spot, volatility, or time:

python

greeks = calculator.instrument_greeks(
    instrument_id=option_id,
    spot_shock=10.0,            # +10 points on underlying
    vol_shock=0.02,             # +2% absolute vol increase
    time_to_expiry_shock=1/365, # roll forward one day
)

Volatility update: refine implied vol from a cached starting point for faster convergence:

python

greeks = calculator.instrument_greeks(
    instrument_id=option_id,
    update_vol=True,        # use cached vol as starting point
    cache_greeks=True,      # store result for next iteration
)

Beta-weighted Greeks: express delta and gamma in terms of an index:

python

greeks = calculator.instrument_greeks(
    instrument_id=option_id,
    index_instrument_id=InstrumentId.from_str("SPX.CBOE"),
    beta_weights={underlying_id: 1.15},
    percent_greeks=True,
)

Time-weighted vega: normalize vega across different expirations:

python

greeks = calculator.instrument_greeks(
    instrument_id=option_id,
    vega_time_weight_base=30,  # normalize to 30-day vega
)

Portfolio Greeks

Aggregate Greeks across all open positions matching filter criteria:

python

portfolio = calculator.portfolio_greeks(
    underlyings=["AAPL", "MSFT"],
    venue=Venue("CBOE"),
    strategy_id=StrategyId("DELTA_HEDGE-001"),
    flat_interest_rate=0.0425,
    index_instrument_id=InstrumentId.from_str("SPX.CBOE"),
    beta_weights=beta_dict,
    percent_greeks=True,
)
# Returns PortfolioGreeks: pnl, price, delta, gamma, vega, theta

Filters:

underlyings: list of symbol prefixes (e.g., ["AAPL"] matches AAPL stock and all AAPL options).
venue: restrict to a single venue.
instrument_id: restrict to a single instrument.
strategy_id: restrict to a single strategy.
side: filter by position side (LONG, SHORT).
greeks_filter: callable that accepts PortfolioGreeks per position; return True to include.

GreeksData

GreeksData is a Python custom data class (@customdataclass) that carries the full context of a single instrument's Greeks computation. It extends Data and supports Arrow serialization, cache storage, and catalog persistence.

Field	Type	Description
`instrument_id`	`InstrumentId`	The instrument.
`is_call`	`bool`	True for call, False for put.
`strike`	`float`	Strike price.
`expiry`	`int`	Expiry date as YYYYMMDD integer.
`expiry_in_days`	`int`	Days to expiry.
`expiry_in_years`	`float`	Years to expiry (days / 365.25).
`multiplier`	`float`	Contract multiplier.
`quantity`	`float`	Position quantity (always 1 from `instrument_greeks`).
`underlying_price`	`float`	Underlying price used in calculation.
`interest_rate`	`float`	Interest rate used.
`cost_of_carry`	`float`	Cost of carry (r - dividend yield; 0 for futures).
`vol`	`float`	Implied volatility.
`pnl`	`float`	PnL relative to position entry (if position provided).
`price`	`float`	Model price.
`delta`	`float`	Delta.
`gamma`	`float`	Gamma.
`vega`	`float`	Vega (dV / 1% vol change).
`theta`	`float`	Theta (daily decay).
`itm_prob`	`float`	In‑the‑money probability.

GreeksData scales to portfolio level via its to_portfolio_greeks() method, which multiplies all values by the contract multiplier. The * operator applies position quantity:

python

position_greeks = signed_qty * instrument_greeks  # returns PortfolioGreeks

PortfolioGreeks

PortfolioGreeks is the aggregated result from portfolio_greeks(). It supports addition (+) for combining positions and scalar multiplication (*) for scaling:

Field	Type	Description
`pnl`	`float`	Aggregate PnL.
`price`	`float`	Aggregate model value.
`delta`	`float`	Portfolio delta.
`gamma`	`float`	Portfolio gamma.
`vega`	`float`	Portfolio vega.
`theta`	`float`	Portfolio theta.

YieldCurveData

YieldCurveData stores an interest rate or dividend yield curve. The GreeksCalculator looks up curves from the cache by currency code (for interest rates) or by underlying instrument ID (for dividend yields).

python

from nautilus_trader.model.greeks_data import YieldCurveData
import numpy as np

curve = YieldCurveData(
    ts_event=0,
    ts_init=0,
    curve_name="USD",
    tenors=np.array([0.25, 0.5, 1.0, 2.0]),
    interest_rates=np.array([0.04, 0.042, 0.045, 0.048]),
)

# Callable: interpolates rate for a given tenor
rate = curve(0.75)  # quadratic interpolation

Choosing between the two paths

Criterion	Venue‑provided (`OptionGreeks`)	Local calculator (`GreeksCalculator`)
Computation	Done by the venue	Local Black‑Scholes
Latency	Arrives with market data	Computed on demand
Venues	Deribit, Bybit, OKX	Any venue with option instruments
Shock scenarios	Not supported	Spot, vol, and time shocks
Portfolio aggregation	Manual (iterate `OptionChainSlice`)	Built‑in via `portfolio_greeks()`
Beta weighting	Not supported	Built‑in
Backtest support	Via recorded `OptionGreeks` data	From cached prices at any point in time
Greeks available	delta, gamma, vega, theta, rho, IV, OI	delta, gamma, vega, theta, itm_prob, vol
Data type	`OptionGreeks` (Rust/PyO3)	`GreeksData` (Python `@customdataclass`)

Greek definitions

For reference, the Greeks that Nautilus computes:

Greek	Symbol	Definition
Delta	`d`	First derivative of option price with respect to underlying price (dV/dS).
Gamma	`g`	Second derivative of option price with respect to underlying price (d2V/dS2).
Vega	`v`	Sensitivity to a 1 percentage point change in implied volatility (dV/dVol).
Theta	`t`	Daily time decay: change in option price per calendar day (dV/dt / 365.25).
Rho	`r`	Sensitivity to a change in the risk‑free interest rate (dV/dr).
ITM prob	-	Probability that the option finishes in the money: P(ϕS_T > ϕK), where ϕ = 1 for calls and ϕ = -1 for puts.

Examples

Complete working examples are available in the repository:

examples/live/bybit/bybit_option_greeks.py: subscribe to Bybit venue-provided Greeks.
examples/live/deribit/deribit_option_greeks.py: subscribe to Deribit venue-provided Greeks.
examples/live/okx/okx_option_greeks.py: subscribe to OKX venue-provided Greeks.

Options - Option instruments, chain subscriptions, and strike filtering.
Data - Built-in data types, custom data, and the subscription model.
Actors - Subscription and handler reference.
Strategies - Strategy implementation and handler methods.

Greeks

Greeks

Venue-provided Greeks (Rust/PyO3)

OptionGreeks

Underlying Rust types

Black-Scholes functions (Rust/PyO3)

Local Greeks calculator (Cython/Python)

GreeksCalculator

Instrument Greeks

Portfolio Greeks

GreeksData

PortfolioGreeks

YieldCurveData

Choosing between the two paths

Greek definitions

Examples

Related guides