abaquant.derivatives.analytics.distributions¶

Import path: abaquant.derivatives.analytics.distributions

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

Purpose¶

Distribution diagnostics and Monte Carlo error analytics.

This module computes derived diagnostics from prices, returns, or model outputs. Ensure inputs use the frequency and units stated by each function.

function: distribution_moments — Compute sample distribution moments used for diagnostics.
function: excess_kurtosis — Compute sample excess kurtosis.
function: theoretical_mc_error — Compute the theoretical Monte Carlo standard-error proxy used by the module.

Distribution diagnostics and Monte Carlo error analytics.

The module computes sample moments and a theoretical standard-error proxy for Monte Carlo valuation.

Sample arrays are interpreted as numerical observations; time is in years and volatility is annualized decimal volatility.

References

[ 1 ] Glasserman, P. (2004), Monte Carlo Methods in Financial Mathematics.

abaquant.derivatives.analytics.distributions.distribution_moments(values)¶

Compute sample distribution moments used for diagnostics.

Parameters:: values (Sequence[float] | np.ndarray) – One-dimensional numerical sample used for distribution diagnostics.
Returns:: Named outputs of the distribution moments calculation.
Return type:: dict[str, float]

abaquant.derivatives.analytics.distributions.excess_kurtosis(values)¶

Compute sample excess kurtosis.

Parameters:: values (Sequence[float] | np.ndarray) – One-dimensional numerical sample used for distribution diagnostics.
Returns:: Computed excess kurtosis as a scalar in the units implied by the input values.
Return type:: float

abaquant.derivatives.analytics.distributions.theoretical_mc_error(reference_price, sigma, T, n_paths)¶

Compute the theoretical Monte Carlo standard-error proxy used by the module.

Parameters:

reference_price (float) – Reference option price used by the Monte Carlo error formula.
sigma (float) – Annualized lognormal volatility in decimal units; for example, 0.20 denotes 20%.
T (float) – Time to maturity in years.
n_paths (Sequence[int] | np.ndarray) – Number of Monte Carlo paths.

Returns:

Result of the theoretical mc error calculation.

Return type:

np.ndarray