Marginal1D

class quantflow.utils.marginal.Marginal1D

Marginal distribution

Methods:

call_option_transform	Call option transform
cdf	Compute the cumulative distribution function
cdf_jacobian	Jacobian of the cdf with respect to the parameters of the process.
characteristic	Compute the characteristic function on support points n.
characteristic_df	Compute the characteristic function with n discretization points and a max frequency
domain_range	The space domain range for the random variable
frequency_range	The frequency domain range for the characteristic function
mean	Expected value
mean_from_characteristic	Calculate mean as first derivative of characteristic function at 0
option_alpha	Option alpha
option_support	Compute the x axis.
option_time_value	Option time value
option_time_value_transform	Option time value transform
pdf	Computes the probability density (or mass) function of the process.
pdf_from_characteristic	Compute the probability density function from the characteristic function.
pdf_jacobian	Jacobian of the pdf with respect to the parameters of the process.
std	Standard deviation at a time horizon
std_from_characteristic	Calculate standard deviation as square root of variance
support	Compute the x axis.
variance	Variance
variance_from_characteristic	Calculate variance as second derivative of characteristic function at 0

Attributes:

model_config

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].

call_option_transform(u: int | float | complex | ndarray | Series) → int | float | complex | ndarray | Series

Call option transform

cdf(x: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Compute the cumulative distribution function

Parameters:

n – Location in the stochastic process domain space. If a numpy array, the output should have the same shape as the input.

cdf_jacobian(x: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray

Jacobian of the cdf with respect to the parameters of the process. It is useful for optimization purposes if necessary.

Optional to implement, otherwise raises NotImplementedError if called.

abstract characteristic(u: int | float | complex | ndarray | Series) → int | float | complex | ndarray | Series

Compute the characteristic function on support points n.

characteristic_df(n: int | None = None, *, max_frequency: float | None = None, simpson_rule: bool = False) → DataFrame

Compute the characteristic function with n discretization points and a max frequency

domain_range() → Bounds

The space domain range for the random variable

This should be overloaded if required

frequency_range(max_frequency: float | None = None) → float

The frequency domain range for the characteristic function

This should be overloaded if required

mean() → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Expected value

This should be overloaded if a more efficient way of computing the mean

mean_from_characteristic(*, d: float = 0.001) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Calculate mean as first derivative of characteristic function at 0

option_alpha() → float

Option alpha

option_support(points: int = 101, max_moneyness: float = 1.0) → ndarray[tuple[int, ...], dtype[floating[Any]]]

Compute the x axis.

option_time_value(n: int = 128, *, max_frequency: float | None = None, max_moneyness: float = 1, alpha: float = 1.1, simpson_rule: bool = False, use_fft: bool = False) → TransformResult

Option time value

option_time_value_transform(u: int | float | complex | ndarray | Series, alpha: float = 1.1) → int | float | complex | ndarray | Series

Option time value transform

This transform does not require any additional correction since the integrant is already bounded for positive and negative moneyess

pdf(x: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Computes the probability density (or mass) function of the process.

It has a base implementation that computes the pdf from the cdf method, but a subclass should overload this method if a more optimized way of computing it is available.

Parameters:

n – Location in the stochastic process domain space. If a numpy array, the output should have the same shape as the input.

pdf_from_characteristic(n: int | None = None, *, max_frequency: float | None = None, simpson_rule: bool = False, use_fft: bool = False, frequency_n: int | None = None) → TransformResult

Compute the probability density function from the characteristic function.

Parameters:

• n – Number of discretization points to use in the transform. If None, use 128.

• max_frequency – The maximum frequency to use in the transform. If not provided, the value from the frequency_range() method is used. Only needed for special cases/testing.

• simpson_rule – Use Simpson’s rule for integration. Default is False.

• use_fft – Use FFT for the transform. Default is False.

pdf_jacobian(x: ndarray[tuple[int, ...], dtype[floating[Any]]] | float) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Jacobian of the pdf with respect to the parameters of the process. It has a base implementation that computes it from the cdf_jacobian method, but a subclass should overload this method if a more optimized way of computing it is available.

std() → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Standard deviation at a time horizon

std_from_characteristic() → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Calculate standard deviation as square root of variance

abstract support(points: int = 100, *, std_mult: float = 3) → ndarray[tuple[int, ...], dtype[floating[Any]]]

Compute the x axis.

variance() → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Variance

This should be overloaded if a more efficient way of computing the

variance_from_characteristic(*, d: float = 0.001) → ndarray[tuple[int, ...], dtype[floating[Any]]] | float

Calculate variance as second derivative of characteristic function at 0

model_config: ClassVar[ConfigDict] = {'extra': 'forbid'}

Configuration for the model, should be a dictionary conforming to [ConfigDict][pydantic.config.ConfigDict].