abaquant.derivatives.trees¶

Import path: abaquant.derivatives.trees

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

Purpose¶

Binomial-lattice option pricing.

When to use it¶

Use this package when valuing contingent claims, calculating Greeks, building option strategies, simulating stochastic processes, or fitting models to market observations.

Public objects¶

function: binomial_tree — Price a vanilla option by backward induction on a binomial lattice.
function: crr_binomial_tree — Price a vanilla option with the Cox–Ross–Rubinstein lattice convention.

Detailed reference¶

Binomial-lattice option pricing.

Purpose¶

This module constructs recombining Cox–Ross–Rubinstein-style trees for vanilla options and can include early exercise by backward induction.

Conventions¶

Maturity is in years, the number of steps is a positive integer, and rates, yields, and volatility are decimal annual quantities.

Scope and limitations¶

Tree values are numerical approximations whose accuracy depends on the number of time steps.

References

[ 1 ] Cox, J. C., S. A. Ross, and M. Rubinstein (1979), “Option Pricing: A Simplified Approach”.

abaquant.derivatives.trees.binomial_tree(S, K, T, r, sigma, n, q=0.0, option_type='call', american=False)¶

Price a vanilla option by backward induction on a binomial lattice.

Parameters:

S (float) – Current underlying spot price in currency units.
K (float) – Option strike price in the same currency units as the underlying.
T (float) – Time to maturity in years.
r (float) – Continuously compounded risk-free annual rate in decimal units.
sigma (float) – Annualized lognormal volatility in decimal units; for example, 0.20 denotes 20%.
n (int) – Number of discrete periods, assets, or observations as determined by the callable.
q (float, default=0.0) – Continuous dividend or carry yield in decimal annual units.
option_type (str, default='call') – Option type label, normally "call" or "put".
american (bool, default=False) – Whether early exercise is allowed in the lattice valuation.

Returns:

Positional outputs produced by the binomial tree calculation.

Return type:

tuple[float, tuple[np.ndarray, np.ndarray] | None]

Notes

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

abaquant.derivatives.trees.crr_binomial_tree(S, K, r, sigma, T, n, is_call=True, american=False, q=0.0)¶

Price a vanilla option with the Cox–Ross–Rubinstein lattice convention.

Parameters:

S (float) – Current underlying spot price in currency units.
K (float) – Option strike price in the same currency units as the underlying.
r (float) – Continuously compounded risk-free annual rate in decimal units.
sigma (float) – Annualized lognormal volatility in decimal units; for example, 0.20 denotes 20%.
T (float) – Time to maturity in years.
n (int) – Number of discrete periods, assets, or observations as determined by the callable.
is_call (bool, default=True) – Whether the instrument is a call; false selects a put.
american (bool, default=False) – Whether early exercise is allowed in the lattice valuation.
q (float, default=0.0) – Continuous dividend or carry yield in decimal annual units.

Returns:

Positional outputs produced by the crr binomial tree calculation.

Return type:

tuple[float, np.ndarray | None, np.ndarray | None]

Notes

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