def test_monte_carlo():
skew1 = skew_normal_density(L=25, unit=unit, a=1.5)
densities = [skew1, skew1, skew1]
densityAll, multiplicityAll = winner_of_many(densities)
densityAllCheck = sample_winner_of_many(densities, nSamples=5000)
assert all(
abs(p1 - p2) < 3e-2 for p1, p2 in zip(densityAll, densityAllCheck))
def demo():
densities = [
skew_normal_density(L=L, unit=unit, a=0.3 * i) for i in range(25)
]
best, multiplicity = winner_of_many(densities)
densitiesPlot([d / unit
for d in densities[:5]] + [best / unit, multiplicity], unit)
def demo():
skew1 = skew_normal_density(L=25, unit=unit, a=1.5)
densities = [skew1, skew1, skew1]
densityAll, multiplicityAll = winner_of_many(densities)
densityAllCheck = sample_winner_of_many(densities, nSamples=50000)
if PLOTS:
densitiesPlot([densityAll, densityAllCheck], unit=0.1)
def demo():
skew1 = skew_normal_density(L=L, unit=unit, a=1.5)
skew2 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-0.5)
skew3 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-1.0)
best, multiplicity = winner_of_many([skew1, skew2, skew3])
densitiesPlot(
[skew1 / unit, skew2 / unit, skew3 / unit, best / unit, multiplicity],
unit,
legend=['1', '2,', '3', 'best', 'multiplicity'])
def test_calibration():
skew1 = skew_normal_density(L=L, unit=unit, a=1.5)
prices = [0.2, 0.3, 0.5]
implied_offsets = solve_for_implied_offsets(prices=prices,
density=skew1,
nIter=2)
inferred_prices = state_prices_from_offsets(skew1, implied_offsets)
print(str(inferred_prices))
densities = densities_from_offsets(skew1, implied_offsets)
densityAllAgain, multiplicityAll = winner_of_many(densities)
def demo():
skew1 = skew_normal_density(L=L, unit = unit, a=1.5)
prices = [ 0.2, 0.3, 0.5 ]
implied_offsets = solve_for_implied_offsets(prices = prices, density = skew1, nIter = 2)
inferred_prices = state_prices_from_offsets( skew1, implied_offsets )
print(str(inferred_prices))
densities = densities_from_offsets( skew1, implied_offsets )
densityAllAgain, multiplicityAll = winner_of_many(densities)
if PLOTS:
densitiesPlot( [ densityAllAgain ] + densities, unit = 0.1, legend = ['guess','analytic','1','2','3'] )
def test_implicit_payoffs():
skew1 = skew_normal_density(L=L, unit=unit, a=1.5)
skew2 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-0.5)
skew3 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-1.0)
densityAll, multiplicityAll = winner_of_many([skew1, skew2, skew3])
payoffs = implicit_state_prices(density=skew1,
densityAll=densityAll,
multiplicityAll=multiplicityAll,
cdf=None,
cdfAll=None,
offsets=None)
def demo():
skew1 = skew_normal_density(L=L, unit=unit, a=1.5)
skew2 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-0.5)
skew3 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-1.0)
densityAll, multiplicityAll = winner_of_many([skew1, skew2, skew3])
payoffs = implicit_state_prices(density=skew1,
densityAll=densityAll,
multiplicityAll=multiplicityAll,
cdf=None,
cdfAll=None,
offsets=None)
import matplotlib.pyplot as plt
plt.plot(payoffs)
plt.show()
def test_minimumPdf():
skew1 = skew_normal_density(L=L, unit=unit, a=1.5)
skew2 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-0.5)
skew3 = skew_normal_density(L=L, unit=unit, a=1.5, loc=-1.0)
best, multiplicity = winner_of_many([skew1, skew2, skew3])
def solve_for_implied_offsets(prices,
density,
offset_samples=None,
implied_offsets_guess=None,
nIter=3,
verbose=False,
visualize=False):
"""
This is the main routine.
See the paper for details, in the /doc folder
https://github.com/microprediction/winning/blob/main/docs/Horse_Race_Problem__SIAM_updated.pdf
offset_samples Optionally supply a list of offsets which are used in the interpolation table a_i -> p_i
"""
L = implied_L(density)
if offset_samples is None:
offset_samples = list(range(int(-L / 2), int(L / 2)))[::-1]
else:
_assert_descending(offset_samples)
if implied_offsets_guess is None:
implied_offsets_guess = list(range(int(L / 3)))
# First guess at densities
densities, coefs = densities_and_coefs_from_offsets(
density, implied_offsets_guess)
densityAllGuess, multiplicityAllGuess = winner_of_many(densities)
densityAll = densityAllGuess.copy()
multiplicityAll = multiplicityAllGuess.copy()
if verbose:
guess_prices = [
np.sum(
expected_payoff(density,
densityAll,
multiplicityAll,
cdf=None,
cdfAll=None)) for density in densities
]
for _ in range(nIter):
if visualize:
from winning.lattice_plot import densitiesPlot
# temporary hack to check progress of optimization
densitiesPlot([densityAll] + densities, unit=0.1)
# Main iteration...
implied_prices = implicit_state_prices(density=density,
densityAll=densityAll,
multiplicityAll=multiplicityAll,
offsets=offset_samples)
implied_offsets = np.interp(prices, implied_prices, offset_samples)
densities = densities_from_offsets(density, implied_offsets)
densityAll, multiplicityAll = winner_of_many(densities)
if verbose:
guess_prices = [
np.sum(
expected_payoff(density,
densityAll,
multiplicityAll,
cdf=None,
cdfAll=None)) for density in densities
]
approx_prices = [np.round(pri, 3) for pri in prices]
approx_guesses = [np.round(pri, 3) for pri in guess_prices]
print(zip(approx_prices, approx_guesses)[:5])
return implied_offsets