abaquant.derivatives.models.bachelier¶

Import path: abaquant.derivatives.models.bachelier

Domain: Derivative pricing, simulation, calibration, diagnostics, and strategy analysis.

Purpose¶

Bachelier normal-volatility option pricing.

When to use it¶

This module implements or supports one derivative model. Read the parameter constraints, pricing measure, numerical method, and limiting cases before comparing outputs across models.

Public objects¶

class: NormalBachelierModel — Bachelier normal-volatility model for European vanilla options. * NormalBachelierModel.call_price — Return the model price of a European call option. * NormalBachelierModel.put_price — Return the model price of a European put option. * NormalBachelierModel.greeks — Return the model sensitivities implemented by this model. * NormalBachelierModel.implied_normal_vol — Return the Bachelier normal implied volatility associated with the model price. * NormalBachelierModel.lognormal_vol — Compute the result defined by ‘’lognormal_vol’’ under this module’s documented convention. * NormalBachelierModel.vol_smile — Evaluate the model-implied volatility across the supplied strike grid. * NormalBachelierModel.visualize — Return a backend-native visualization of this option-pricing model.

Detailed reference¶

Bachelier normal-volatility option pricing.

Purpose¶

The module implements European option prices and Greeks under a normally distributed discounted underlying.

Conventions¶

Normal volatility has price units per square-root year. Rates and continuous dividend yields are decimal annual rates; maturity is in years.

References

[ 1 ] Bachelier, L. (1900), “Theorie de la Speculation”.

class abaquant.derivatives.models.bachelier.NormalBachelierModel(spot_price, strike_price, maturity_years, risk_free_rate, normal_volatility, dividend_yield=0.0)¶

Bases: OptionDiagnosticsMixin

Bachelier normal-volatility model for European vanilla options.

Parameters:

spot_price (float or array-like) – Current underlying asset price in currency units.
strike_price (float or array-like) – Option exercise price in currency units.
maturity_years (float or array-like) – Time to expiration in years.
risk_free_rate (float or array-like) – Continuously compounded annual risk-free rate in decimal units.
normal_volatility (float or array-like) – Annualized normal volatility in price units per square-root year.
dividend_yield (float, default=0.0) – Continuously compounded annual dividend or carry yield in decimal units.

Initialize the Bachelier normal-volatility model state.

Parameters:

spot_price (float or array-like) – Current underlying asset price in currency units.
strike_price (float or array-like) – Option exercise price in currency units.
maturity_years (float or array-like) – Time to expiration in years.
risk_free_rate (float or array-like) – Continuously compounded annual risk-free rate in decimal units.
normal_volatility (float or array-like) – Annualized normal volatility in price units per square-root year.
dividend_yield (float, default=0.0) – Continuously compounded annual dividend or carry yield in decimal units.

call_price()¶

Return the model price of a European call option.

Returns:: Computed call price in the units implied by the documented inputs.
Return type:: float

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.

put_price()¶

Return the model price of a European put option.

Returns:: Computed put price in the units implied by the documented inputs.
Return type:: float

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.

greeks()¶

Return the model sensitivities implemented by this model.

Returns:: Result of the greeks workflow.
Return type:: object

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.

implied_normal_vol(market_price, option_type='call', tol=1e-8)¶

Return the Bachelier normal implied volatility associated with the model price.

Parameters:

market_price (float or array-like) – Observed option premium in the same currency units as spot and strike.
option_type (str, default='call') – Option type label, normally "call" or "put".
tol (float, default=1e-08) – Numerical convergence tolerance.

Returns:

Result of the implied normal vol workflow.

Return type:

object

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.

lognormal_vol()¶

Compute the result defined by lognormal_vol under this module’s documented convention.

Returns:: Result of the lognormal vol workflow.
Return type:: object

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.

vol_smile(strikes)¶

Evaluate the model-implied volatility across the supplied strike grid.

Parameters:: strikes (float or array-like) – Strike-price grid in the same currency units as the underlying or forward.
Returns:: Numeric array ordered consistently with the supplied strikes, time grid, assets, or state labels.
Return type:: numpy.ndarray

Notes

Model inputs are interpreted according to the module-level rate, maturity, and volatility conventions. Numerical outputs depend on the validity of those assumptions.

visualize(*, option_type='call', chart='payoff', backend=None, theme=None, save_path=None, filename=None, lower_spot_multiple=0.5, upper_spot_multiple=1.5, grid_size=101, lower_volatility_multiple=0.5, upper_volatility_multiple=1.5, volatility_grid_size=31, greek_scale='raw')¶

Return a backend-native visualization of this option-pricing model.

Parameters:

option_type ({"call", "put"}, default="call") – Vanilla option type used for payoff, price-profile, smile, or tree plots.
chart (str, default="payoff") – Visual diagnostic to create. Supported charts include payoff, price profile, extrinsic value, Greek curves, selected surfaces, volatility smile, and lattice tree when the model exposes a tree.
backend ({"matplotlib", "plotly"}, default="matplotlib") – Optional plotting backend. The returned figure is not shown automatically.
lower_spot_multiple (float, default=0.5, 1.5) – Price-grid bounds as multiples of the strike price.
upper_spot_multiple (float, default=0.5, 1.5) – Price-grid bounds as multiples of the strike price.
grid_size (int, default=101) – Number of spot-grid points for non-tree plots.
lower_volatility_multiple (float, default=0.5, 1.5) – Volatility-grid bounds expressed as multiples of the model’s base volatility.
upper_volatility_multiple (float, default=0.5, 1.5) – Volatility-grid bounds expressed as multiples of the model’s base volatility.
volatility_grid_size (int, default=31) – Number of volatility-grid points for surface plots.
greek_scale ({"raw", "standardized"}, default="raw") – Scaling mode for the multi-Greek curve chart.

Returns:

Figure object created without mutating model state.

Return type:

matplotlib.figure.Figure or plotly.graph_objects.Figure