al6x

using Random, Distributions, Statistics, DataFrames, Plots

# parameters
Random.seed!(1)
mu = 0.005             # drift per 30d step
sigma = 0.08           # volatility per step
steps = 12 * 45 * 250  # number of 30d steps
S0 = 1.0               # initial price
ν = 3                  # degrees of freedom for Student-t (ν > 2)

al6x

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import t
from scipy.optimize import minimize_scalar, minimize

def student_sample(df, n, seed=None):
  rng = np.random.default_rng(seed)
  return rng.standard_t(df, size=n)

def estimate_hill(x):

al6x

import numpy as np
import matplotlib.pyplot as plt
from scipy.stats import t
from scipy.optimize import minimize_scalar

def student_sample(df, n):
  return t.rvs(df, loc=0, scale=1, size=n)

def estimate_hill(x):
  x = np.sort(x)[::-1]

al6x

al6x

import pandas as pd
import numpy as np
from scipy.integrate import quad
from scipy.stats import norm
import matplotlib.pyplot as plt
import math

def data_stats():
  # Distrs as (weights, scales_rel) where scales_rel - relative to the main scale

al6x

import pandas as pd
import matplotlib.pyplot as plt
import numpy as np
from matplotlib.ticker import FuncFormatter, LogLocator

# Data:
#   lr_rf_1y_t   : float  — risk-free log return at time t (e.g., log(1.03) for 3%)
#   lr_t2        : float  — stock actual log return at time t2 = t + period_d
#   ema_var_d_t  : float  — daily variance as log(return)^2, current estimate at time t as EMA(span=365/3)
#   h_var_d      : float  — daily variance as log(return)^2, historical estimate over whole stock history

al6x

import './base'

p_([1, 2, 2].empty7())                       // => false

p_([[2], [1]].sort_())                       // => [[1], [2]]
p_([[1], [1]].uniq_())                       // => [[1]]
p_(equal7([1], [1]))                         // => true
p_([1, 2, 3].median_())                      // => 2
p_([1, 2, 3].min_())                         // => 1

al6x

import pymc as pm
import arviz as az

def fit_bayesian_slow(df, t):
  r_t = df['r_t'].values
  mvar_t_t0 = t * 0.69 * df['mvar_d_t0'].values
  r_rf_t_t0 = t * np.log(df['ar_rf_1y_t0'].values) / 365

  with pm.Model() as model:
    v0 = pm.HalfNormal('v0', sigma=1)

al6x

[0.07662950232169972, 0.08667983817520133, 0.08667983817520133, 0.08667983817520133, 0.18199001797952605, 0.2690013949691558, 0.1636408793113296, 0.18199001797952605, 0.18199001797952605, 0.07662950232169972, 0.07662950232169972, 0.18199001797952605, 0.18199001797952605, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.06833069950700488, 0.06833069950700488, 0.06833069950700488, 0.06833069950700488, 0.06833069950700488, 0.06833069950700488, 0.06833069950700488, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.07662950232169972, 0.08667983817520133, 0.06833069950700488, 0.1636408793113296, 0.1636408793113296, 0.1636408793113296, 0.1636408793113296, 0.2436835869848659, 0.2436835869848659, 0.

al6x

import numpy as np
import matplotlib.pyplot as plt
from sklearn.mixture import GaussianMixture
from scipy.stats import norm

def fit_normal_mixture(*, n_components, values, random_state, n_init):
    values = np.array(values).reshape(-1, 1)  # Convert to 2D array
    nmm = GaussianMixture(n_components, covariance_type='diag', random_state=random_state, n_init=n_init)
    nmm.fit(values)
    means = nmm.means_.flatten().tolist()