# AnalyticalConeBase¶

class `qf_lib.common.utils.confidence_interval.analytical_cone_base.``AnalyticalConeBase`[source]

Bases: `object`

Methods

 `calculate_simple_cone_for_process`(mu, sigma, …) Creates a simple cone starting from a given date using the solution to the stochastic equation: `get_expected_value`(mu, sigma, …) For the mu and sigma calculated based on log returns:
`calculate_simple_cone_for_process`(mu: float, sigma: float, number_of_std: float, number_of_steps: int, starting_value=1)qf_lib.containers.series.prices_series.PricesSeries[source]

Creates a simple cone starting from a given date using the solution to the stochastic equation: S(t) = S(0)*exp( (mu-0.5*sigma^2)*t + sigma*N(0,1)*sqrt(t) )

Parameters
• mu – mean return of the process. expressed in the frequency of samples (not annualised)

• sigma – std of returns of the process. expressed in the frequency of samples (not annualised)

• number_of_std – corresponds to the randomness of the stochastic process. reflects number of standard deviations to get expected values for. For example 1.0 means 1 standard deviation above the expected value.

• number_of_steps – length of the cone that we are creating

• starting_value – corresponds to the starting price of the instrument

Returns

expected values

Return type

PriceSeries

static `get_expected_value`(mu, sigma, starting_price, number_of_steps, random_element) → float[source]
For the mu and sigma calculated based on log returns:

S(t) = S(0)*exp( (mu-0.5*sigma^2)*t + sigma*N(0,1)*sqrt(t))

Parameters
• mu – mean of the distribution of returns

• sigma – standard deviation of the returns

• starting_price – price of the stock at the beginning of the cone

• number_of_steps – horizon for which the expected value is calculated

• random_element – corresponds to the N(0,1). is expressed in number of standard deviations. Use 1 to model 1std up move, Use 0 to model expected vale of the stock

Returns

Expected value of the stock after number_of_steps given the input parameters

Return type

float