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():
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=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 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'] )
from winning.lattice import densities_from_events, state_prices_from_densities
from winning.lattice_plot import densitiesPlot
def test_golf():
event_18 = [0, 0, 0.5, 0.5, 0, 0, 0]
event_17 = [0, 0, 0.5, 0.5, 0, 0, 0]
scores = [-15, -15]
densities = densities_from_events(scores=scores,
events=[[event_17, event_18],
[event_18]],
unit=1,
L=6)
return densities
if __name__ == '__main__':
d = test_golf()
import matplotlib.pyplot as plt
densitiesPlot(d, unit=1, legend=['two to play', 'one to play'])
plt.show()
p = state_prices_from_densities(densities=d)
print(p)
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
from winning.lattice_copula import gaussian_copula_margin_0
from winning.lattice import skew_normal_density
from winning.lattice_plot import densitiesPlot
from pprint import pprint
def test_ensure_scipy():
from winning.scipyinclusion import using_scipy
from scipy.integrate import quad_vec
assert using_scipy
def test_five_skew():
mus = [-0.5, -0.25, 0, 1, 1.5]
scales = [1.0, 1.5, 1.2, 1.3, 2.0]
densities = [skew_normal_density(L=500, unit=0.01, scale=scale, loc=mu, a=1.0) for mu, scale in zip(mus, scales)]
margin_0 = gaussian_copula_margin_0(densities, rho=0.9)
return densities[0], margin_0
if __name__=='__main__':
density1, density2 = test_five_skew()
legend = ['margin','reconstructed']
densitiesPlot(densities=[density1,density2], unit=0.1, legend=legend)
print(sum(density2))
def demo():
skew = skew_normal_density(L=L, unit=unit, a=1.0)
print("mean is " + str(mean_of_density(skew, unit=unit)))
densitiesPlot([skew], unit=unit)
from winning.lattice import skew_normal_density
from winning.lattice_plot import densitiesPlot
from pprint import pprint
def test_ensure_scipy():
from winning.scipyinclusion import using_scipy
from scipy.integrate import quad_vec
assert using_scipy
def test_five_skew():
mus = [-0.5, -0.25, 0, 1, 1.5]
scales = [1.0, 1.5, 1.2, 1.3, 2.0]
densities = [
skew_normal_density(L=100, unit=0.1, scale=scale, loc=mu, a=1.0)
for mu, scale in zip(mus, scales)
]
rank_probs = gaussian_copula_five(densities, rho=0.01)
return densities, rank_probs
if __name__ == '__main__':
import time
st = time.time()
densities, rank_probs = test_five_skew()
legend = ['Asset ' + str(i) for i in range(1, 6)]
print({'elapsed': time.time() - st})
densitiesPlot(densities=densities, unit=0.1, legend=legend)
pprint(rank_probs)
from winning.lattice_copula import gaussian_copula_win
from winning.lattice import skew_normal_density
from winning.lattice_plot import densitiesPlot
def test_ensure_scipy():
from winning.scipyinclusion import using_scipy
assert using_scipy
def test_two_skew():
density1 = skew_normal_density(L=50, unit=0.1, scale=1.0, loc=1.0, a=1.0)
density2 = skew_normal_density(L=50, unit=0.1, scale=1.0, loc=0, a=1.0)
densities = [density1, density2]
state_prices = gaussian_copula_win(densities=densities, rho=0.85)
return densities, state_prices
if __name__ == '__main__':
densities, state_prices = test_two_skew()
densitiesPlot(densities=densities, unit=0.1)
print(state_prices)