def get_one_sample_score(self, q, free_parameters, seed_index):
free_para1 = free_parameters['cov_para_1']
free_para2 = free_parameters['cov_para_2']
free_para3 = free_parameters['cov_para_3']
free_para4 = free_parameters['cov_para_4']
free_para5 = free_parameters['cov_para_5']
free_para6 = free_parameters['cov_para_6']
free_para7 = free_parameters['cov_para_7']
free_para8 = free_parameters['cov_para_8']
free_para9 = free_parameters['cov_para_9']
free_para10 = free_parameters['cov_para_10']
free_para11 = free_parameters['cov_para_11']
free_para12 = free_parameters['cov_para_12']
free_para13 = free_parameters['cov_para_13']
free_para14 = free_parameters['cov_para_14']
free_para15 = free_parameters['cov_para_15']
diag_1 = 1
diag_2 = np.sqrt(1 - free_para1**2)
if (1 - free_para2**2 - free_para3**2) < 0:
diag_3 = np.sqrt(np.abs(1 - free_para2**2 - free_para3**2))
else:
diag_3 = np.sqrt(1 - free_para2**2 - free_para3**2)
if (1 - free_para4**2 - free_para5**2 - free_para6**2) < 0:
diag_4 = np.sqrt(
np.abs(1 - free_para4**2 - free_para5**2 - free_para6**2))
else:
diag_4 = np.sqrt(1 - free_para4**2 - free_para5**2 - free_para6**2)
if (1 - free_para7**2 - free_para8**2 - free_para9**2 -
free_para10**2) < 0:
diag_5 = np.sqrt(
np.abs(1 - free_para7**2 - free_para8**2 - free_para9**2 -
free_para10**2))
else:
diag_5 = np.sqrt(1 - free_para7**2 - free_para8**2 -
free_para9**2 - free_para10**2)
if (1 - free_para11**2 - free_para12**2 - free_para13**2 -
free_para14**2 - free_para15**2) < 0:
diag_6 = np.sqrt(
np.abs(1 - free_para11**2 - free_para12**2 - free_para13**2 -
free_para14**2 - free_para15**2))
else:
diag_6 = np.sqrt(1 - free_para11**2 - free_para12**2 -
free_para13**2 - free_para14**2 - free_para15**2)
lower_triangular_matrix = np.asarray(
[[diag_1, 0, 0, 0, 0, 0], [free_para1, diag_2, 0, 0, 0, 0],
[free_para2, free_para3, diag_3, 0, 0, 0],
[free_para4, free_para5, free_para6, diag_4, 0, 0],
[free_para7, free_para8, free_para9, free_para10, diag_5, 0],
[
free_para11, free_para12, free_para13, free_para14,
free_para15, diag_6
]])
cov_matrix = lower_triangular_matrix @ lower_triangular_matrix.transpose(
)
#now, define the marginal distribution of the gaussian copula
univerates = [{
'loc': 0,
'scale': 1,
'a': free_parameters['beta_1a'],
'b': free_parameters['beta_1b'],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': free_parameters['beta_2a'],
'b': free_parameters['beta_2b'],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': free_parameters['beta_3a'],
'b': free_parameters['beta_3b'],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': free_parameters['beta_4a'],
'b': free_parameters['beta_4b'],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': free_parameters['beta_5a'],
'b': free_parameters['beta_5b'],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': free_parameters['beta_6a'],
'b': free_parameters['beta_6b'],
'type': 'copulas.univariate.beta.BetaUnivariate'
}]
#now, we construct the gaussian copula
copula_parameters = {}
copula_parameters['covariance'] = cov_matrix
copula_parameters['univariates'] = univerates
copula_parameters[
'type'] = 'copulas.multivariate.gaussian.GaussianMultivariate'
copula_parameters['columns'] = [0, 1, 2, 3, 4, 5]
new_dist = Multivariate.from_dict(copula_parameters)
#other parameters needed for transforming the features
lambda_expon_1 = free_parameters['lambda_expon_1']
lambda_expon_2 = free_parameters['lambda_expon_2']
lambda_expon_3 = free_parameters['lambda_expon_3']
lambda_expon_4 = free_parameters['lambda_expon_4']
lambda_expon_5 = free_parameters['lambda_expon_5']
lambda_expons = [
lambda_expon_1, lambda_expon_2, lambda_expon_3, lambda_expon_4,
lambda_expon_5
]
#now, we begin to simulate trading
#first, initialize the observation
locol_env = trading_vix_non_random_seed.trading_vix(seed_index)
this_trajectory_reward = []
has_at_least_sell = False
null_objective = True
current_feature = locol_env.reset()
for time_index in range(0, 200):
#compute an action given current observation
transformed_features = []
for feature_index in range(len(lambda_expons)):
transformation = expon.cdf(current_feature[feature_index, 0],
scale=1.0 /
lambda_expons[feature_index])
min_transformation = 0.1
transformation = min_transformation * np.exp(
np.log(1.0 / min_transformation) * transformation)
transformed_features.append(transformation)
transformed_features = np.asarray(transformed_features)
transformed_features = np.reshape(transformed_features, (1, -1))
holding_position = current_feature[-1, :][0]
if holding_position < 0:
print(
'holding is less than 0, there is some problem and the holding position is',
holding_position)
if holding_position > 1:
print(
'holding is greater than 1, there is some problem and the holding position is',
holding_position)
min_transformed_holding = 0.1
transformed_holding = min_transformed_holding * np.exp(
np.log(1.0 / min_transformed_holding) * holding_position)
transformed_holding = np.reshape(transformed_holding, (1, 1))
data_point_for_df = np.concatenate(
(transformed_features, transformed_holding), axis=1)
assert data_point_for_df.shape[1] == 6
data_point_for_copula = pd.DataFrame(data_point_for_df)
action = new_dist.cdf(data_point_for_copula)
#print('action in optimization trading vix is',action)
#apply the action to the environment
current_feature, reward, has_at_least_sell = locol_env.step(action)
if has_at_least_sell and null_objective:
#print('sold at least once')
null_objective = False
#record reward
this_trajectory_reward.append(reward)
#final time step,get the long term reward
reward = locol_env.final()
this_trajectory_reward.append(reward)
if null_objective:
objective = -1e9
else:
objective = np.sum(this_trajectory_reward)
q.put([objective])
def construct_a_copula(cov_input, marginal_input):
assert len(cov_input) < 4
if len(cov_input) == 3:
diag_1 = 1
diag_2 = np.sqrt(1 - cov_input[0]**2)
if (1 - cov_input[1]**2 - cov_input[2]**2) < 0:
diag_3 = np.sqrt(np.abs(1 - cov_input[1]**2 - cov_input[2]**2))
else:
diag_3 = np.sqrt(1 - cov_input[1]**2 - cov_input[2]**2)
lower_triangular_matrix = np.asarray(
[[diag_1, 0, 0], [cov_input[0], diag_2, 0],
[cov_input[1], cov_input[2], diag_3]])
cov_matrix = lower_triangular_matrix @ lower_triangular_matrix.transpose(
)
if len(cov_input) == 1:
diag_1 = 1
diag_2 = np.sqrt(1 - cov_input[0]**2)
lower_triangular_matrix = np.asarray([[diag_1, 0],
[cov_input[0], diag_2]])
cov_matrix = lower_triangular_matrix @ lower_triangular_matrix.transpose(
)
if len(marginal_input) == 6:
univerates = [{
'loc': 0,
'scale': 1,
'a': marginal_input[0],
'b': marginal_input[1],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': marginal_input[2],
'b': marginal_input[3],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': marginal_input[4],
'b': marginal_input[5],
'type': 'copulas.univariate.beta.BetaUnivariate'
}]
if len(marginal_input) == 4:
univerates = [{
'loc': 0,
'scale': 1,
'a': marginal_input[0],
'b': marginal_input[1],
'type': 'copulas.univariate.beta.BetaUnivariate'
}, {
'loc': 0,
'scale': 1,
'a': marginal_input[2],
'b': marginal_input[3],
'type': 'copulas.univariate.beta.BetaUnivariate'
}]
copula_parameters = {}
copula_parameters['covariance'] = cov_matrix
copula_parameters['univariates'] = univerates
copula_parameters[
'type'] = 'copulas.multivariate.gaussian.GaussianMultivariate'
if len(marginal_input) == 6:
copula_parameters['columns'] = [0, 1, 2]
if len(marginal_input) == 4:
copula_parameters['columns'] = [0, 1]
new_dist = Multivariate.from_dict(copula_parameters)
return new_dist