Module pyfx.pricingscience.elasticity

Functions and utilities for elasticity.

Functions

def elasticity(prices: Union[numpy._typing._array_like._SupportsArray[numpy.dtype[Any]], numpy._typing._nested_sequence._NestedSequence[numpy._typing._array_like._SupportsArray[numpy.dtype[Any]]], bool, int, float, complex, str, bytes, numpy._typing._nested_sequence._NestedSequence[Union[bool, int, float, complex, str, bytes]]], quantities: Union[numpy._typing._array_like._SupportsArray[numpy.dtype[Any]], numpy._typing._nested_sequence._NestedSequence[numpy._typing._array_like._SupportsArray[numpy.dtype[Any]]], bool, int, float, complex, str, bytes, numpy._typing._nested_sequence._NestedSequence[Union[bool, int, float, complex, str, bytes]]], elasticity_func: Callable[..., numpy.ndarray[Any, numpy.dtype[numpy.float64]]] = <function logistic_curve>, log_price: bool = True, log_quantity: bool = True, curve_fit_parameters: Optional[dict[str, typing.Any]] = None, starting_point: Optional[list[typing.Any]] = None) ‑> tuple[numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]], pandas.core.frame.DataFrame]

Fit the elasticity function parameters for the given data.

By default the elasticity function used is the logistic curve (S-curve).

This function uses scipy.optimize.curve_fit. If the elasticity function used is supported, some default curve_fit parameters and starting point will be used. Those can be overrided using the corresponding optional arguments of the function.

Args

prices

the prices data

quantities

the corresponding quantities levels

elasticity_func

the elasticity function to used (default: logistic_curve())

log_price

should the prices be converted to log-base (default: True)

log_quantity

should the demands be converted to log-base (default: True)

curve_fit_parameters

optional parameters for the curve fitting (default: None)

starting_point

optional starting for the curve fitting (default: None)

Returns

A tuple containing: - an array with the fitted function parameter value - a DataFrame with the price, quantity, and computed quantity

def logistic_curve(x: numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]], max_value: float, x0: float, k: float, b: float) ‑> numpy.ndarray[typing.Any, numpy.dtype[numpy.float64]]

Implementation of the logistic curve function (or S-curve).

Args

x

the x value(s)

max_value : also called L

the supremum of the value of the functions

x0

the x value of the function's midpoint

k

the logistic growth rate

b

a constant shift value

Returns

The computed y value(s)