def test_asian_barrier_spread(self):
"""Test the asian barrier spread model."""
try:
from qiskit.aqua.circuits import WeightedSumOperator, FixedValueComparator as Comparator
from qiskit.aqua.components.uncertainty_problems import (
UnivariatePiecewiseLinearObjective as PwlObjective,
MultivariateProblem)
from qiskit.aqua.components.uncertainty_models import MultivariateLogNormalDistribution
except ImportError:
import warnings
warnings.warn(
'Qiskit Aqua is not installed, skipping the application test.')
return
# number of qubits per dimension to represent the uncertainty
num_uncertainty_qubits = 2
# parameters for considered random distribution
spot_price = 2.0 # initial spot price
volatility = 0.4 # volatility of 40%
interest_rate = 0.05 # annual interest rate of 5%
time_to_maturity = 40 / 365 # 40 days to maturity
# resulting parameters for log-normal distribution
# pylint: disable=invalid-name
mu = ((interest_rate - 0.5 * volatility**2) * time_to_maturity +
np.log(spot_price))
sigma = volatility * np.sqrt(time_to_maturity)
mean = np.exp(mu + sigma**2 / 2)
variance = (np.exp(sigma**2) - 1) * np.exp(2 * mu + sigma**2)
stddev = np.sqrt(variance)
# lowest and highest value considered for the spot price; in between,
# an equidistant discretization is considered.
low = np.maximum(0, mean - 3 * stddev)
high = mean + 3 * stddev
# map to higher dimensional distribution
# for simplicity assuming dimensions are independent and identically distributed)
dimension = 2
num_qubits = [num_uncertainty_qubits] * dimension
low = low * np.ones(dimension)
high = high * np.ones(dimension)
mu = mu * np.ones(dimension)
cov = sigma**2 * np.eye(dimension)
# construct circuit factory
distribution = MultivariateLogNormalDistribution(num_qubits=num_qubits,
low=low,
high=high,
mu=mu,
cov=cov)
# determine number of qubits required to represent total loss
weights = []
for n in num_qubits:
for i in range(n):
weights += [2**i]
num_sum_qubits = WeightedSumOperator.get_required_sum_qubits(weights)
# create circuit factoy
agg = WeightedSumOperator(sum(num_qubits), weights)
# set the strike price (should be within the low and the high value of the uncertainty)
strike_price_1 = 3
strike_price_2 = 4
# set the barrier threshold
barrier = 2.5
# map strike prices and barrier threshold from [low, high] to {0, ..., 2^n-1}
max_value = 2**num_sum_qubits - 1
low_ = low[0]
high_ = high[0]
mapped_strike_price_1 = (strike_price_1 - dimension*low_) / \
(high_ - low_) * (2**num_uncertainty_qubits - 1)
mapped_strike_price_2 = (strike_price_2 - dimension*low_) / \
(high_ - low_) * (2**num_uncertainty_qubits - 1)
mapped_barrier = (barrier -
low) / (high - low) * (2**num_uncertainty_qubits - 1)
conditions = []
for i in range(dimension):
# target dimension of random distribution and corresponding condition
conditions += [(i,
Comparator(num_qubits[i],
mapped_barrier[i] + 1,
geq=False))]
# set the approximation scaling for the payoff function
c_approx = 0.25
# setup piecewise linear objective fcuntion
breakpoints = [0, mapped_strike_price_1, mapped_strike_price_2]
slopes = [0, 1, 0]
offsets = [0, 0, mapped_strike_price_2 - mapped_strike_price_1]
f_min = 0
f_max = mapped_strike_price_2 - mapped_strike_price_1
bull_spread_objective = PwlObjective(num_sum_qubits, 0, max_value,
breakpoints, slopes, offsets,
f_min, f_max, c_approx)
# define overall multivariate problem
asian_barrier_spread = MultivariateProblem(distribution,
agg,
bull_spread_objective,
conditions=conditions)
num_req_qubits = asian_barrier_spread.num_target_qubits
num_req_ancillas = asian_barrier_spread.required_ancillas()
qr = QuantumRegister(num_req_qubits, name='q')
qr_ancilla = QuantumRegister(num_req_ancillas, name='q_a')
qc = QuantumCircuit(qr, qr_ancilla)
asian_barrier_spread.build(qc, qr, qr_ancilla)
job = execute(qc,
backend=BasicAer.get_backend('statevector_simulator'))
# evaluate resulting statevector
value = 0
for i, amplitude in enumerate(job.result().get_statevector()):
b = ('{0:0%sb}' % asian_barrier_spread.num_target_qubits
).format(i)[-asian_barrier_spread.num_target_qubits:]
prob = np.abs(amplitude)**2
if prob > 1e-4 and b[0] == '1':
value += prob
# all other states should have zero probability due to ancilla qubits
if i > 2**num_req_qubits:
break
# map value to original range
mapped_value = asian_barrier_spread.value_to_estimation(value) / (
2**num_uncertainty_qubits - 1) * (high_ - low_)
expected = 0.83188
self.assertAlmostEqual(mapped_value, expected, places=5)
def test_conditional_value_at_risk(self, simulator):
""" conditional value at risk test """
# define backend to be used
backend = BasicAer.get_backend(simulator)
# set problem parameters
n_z = 2
z_max = 2
# z_values = np.linspace(-z_max, z_max, 2 ** n_z)
p_zeros = [0.15, 0.25]
rhos = [0.1, 0.05]
lgd = [1, 2]
k_l = len(p_zeros)
# alpha = 0.05
# set var value
var = 2
var_prob = 0.961940
# determine number of qubits required to represent total loss
# n_s = WeightedSumOperator.get_required_sum_qubits(lgd)
# create circuit factory (add Z qubits with weight/loss 0)
agg = WeightedSumOperator(n_z + k_l, [0] * n_z + lgd)
# define linear objective
breakpoints = [0, var]
slopes = [0, 1]
offsets = [0, 0] # subtract VaR and add it later to the estimate
f_min = 0
f_max = 3 - var
c_approx = 0.25
# construct circuit factory for uncertainty model (Gaussian Conditional Independence model)
gci = GCI(n_z, z_max, p_zeros, rhos)
cvar_objective = PwlObjective(
agg.num_sum_qubits,
0,
2**agg.num_sum_qubits -
1, # max value that can be reached by the qubit register
breakpoints,
slopes,
offsets,
f_min,
f_max,
c_approx)
multivariate_cvar = MultivariateProblem(gci, agg, cvar_objective)
num_qubits = multivariate_cvar.num_target_qubits
num_ancillas = multivariate_cvar.required_ancillas()
q = QuantumRegister(num_qubits, name='q')
q_a = QuantumRegister(num_ancillas, name='q_a')
qc = QuantumCircuit(q, q_a)
multivariate_cvar.build(qc, q, q_a)
job = execute(qc, backend=backend)
# evaluate resulting statevector
value = 0
for i, a_i in enumerate(job.result().get_statevector()):
b = ('{0:0%sb}' %
multivariate_cvar.num_target_qubits).\
format(i)[-multivariate_cvar.num_target_qubits:]
a_m = np.round(np.real(a_i), decimals=4)
if np.abs(a_m) > 1e-6 and b[0] == '1':
value += a_m**2
# normalize and add VaR to estimate
value = multivariate_cvar.value_to_estimation(value)
normalized_value = value / (1.0 - var_prob) + var
# compare to precomputed solution
self.assertEqual(0.0, np.round(normalized_value - 3.3796, decimals=4))
def setUp(self):
super().setUp()
# number of qubits to represent the uncertainty
num_uncertainty_qubits = 3
# parameters for considered random distribution
s_p = 2.0 # initial spot price
vol = 0.4 # volatility of 40%
r = 0.05 # annual interest rate of 4%
t_m = 40 / 365 # 40 days to maturity
# resulting parameters for log-normal distribution
m_u = ((r - 0.5 * vol**2) * t_m + np.log(s_p))
sigma = vol * np.sqrt(t_m)
mean = np.exp(m_u + sigma**2 / 2)
variance = (np.exp(sigma**2) - 1) * np.exp(2 * m_u + sigma**2)
stddev = np.sqrt(variance)
# lowest and highest value considered for the spot price;
# in between, an equidistant discretization is considered.
low = np.maximum(0, mean - 3 * stddev)
high = mean + 3 * stddev
# construct circuit factory for uncertainty model
uncertainty_model = LogNormalDistribution(num_uncertainty_qubits,
mu=m_u,
sigma=sigma,
low=low,
high=high)
# set the strike price (should be within the low and the high value of the uncertainty)
strike_price = 1.896
# set the approximation scaling for the payoff function
c_approx = 0.1
# setup piecewise linear objective function
breakpoints = [uncertainty_model.low, strike_price]
slopes = [0, 1]
offsets = [0, 0]
f_min = 0
f_max = uncertainty_model.high - strike_price
european_call_objective = PwlObjective(
uncertainty_model.num_target_qubits, uncertainty_model.low,
uncertainty_model.high, breakpoints, slopes, offsets, f_min, f_max,
c_approx)
# construct circuit factory for payoff function
self.european_call = UnivariateProblem(uncertainty_model,
european_call_objective)
# construct circuit factory for payoff function
self.european_call_delta = EuropeanCallDelta(
uncertainty_model,
strike_price=strike_price,
)
self._statevector = QuantumInstance(
backend=BasicAer.get_backend('statevector_simulator'),
seed_simulator=2,
seed_transpiler=2)
self._qasm = QuantumInstance(
backend=BasicAer.get_backend('qasm_simulator'),
shots=100,
seed_simulator=2,
seed_transpiler=2)
def __init__(self, value, spot_price, volatility, int_rate, days,
strike_price):
self.value = value
# Number of qubits to represent the uncertainty
num_uncertainty_qubits = 3
# Parameters
try:
S = float(spot_price)
vol = float(volatility)
r = float(int_rate)
T = int(days) / 365
strike_price = float(strike_price)
except ValueError:
print("Some parameters wrong !!! ")
mu = ((r - 0.5 * vol**2) * T + np.log(S))
sigma = vol * np.sqrt(T)
mean = np.exp(mu + sigma**2 / 2)
variance = (np.exp(sigma**2) - 1) * np.exp(2 * mu + sigma**2)
stddev = np.sqrt(variance)
low = np.maximum(0, mean - 3 * stddev)
high = mean + 3 * stddev
# Circuit factory for uncertainty model
self.uncertainty_model = LogNormalDistribution(num_uncertainty_qubits,
mu=mu,
sigma=sigma,
low=low,
high=high)
try:
self.strike_price = float(strike_price)
except ValueError:
print("Some parameters wrong !!! ")
# The approximation scaling for the payoff function
c_approx_payoff = 0.25 #abs(S-self.strike_price)
print(c_approx_payoff)
breakpoints = [self.uncertainty_model.low, self.strike_price]
if self.value == str("call"):
slopes_payoff = [0, 1]
else:
slopes_payoff = [-1, 0]
if self.value == str("call"):
offsets_payoff = [0, 0]
else:
offsets_payoff = [
self.strike_price - self.uncertainty_model.low, 0
]
f_min_payoff = 0
if self.value == str("call"):
f_max_payoff = self.uncertainty_model.high - self.strike_price
else:
f_max_payoff = self.strike_price - self.uncertainty_model.low
european_objective = PwlObjective(
self.uncertainty_model.num_target_qubits,
self.uncertainty_model.low, self.uncertainty_model.high,
breakpoints, slopes_payoff, offsets_payoff, f_min_payoff,
f_max_payoff, c_approx_payoff)
# Circuit factory for payoff function
self.european_payoff = UnivariateProblem(self.uncertainty_model,
european_objective)
slopes_delta = [0, 0]
if self.value == str("call"):
offsets_delta = [0, 1]
else:
offsets_delta = [1, 0]
f_min_delta = 0
f_max_delta = 1
c_approx_delta = 1
european_delta_objective = PwlObjective(
self.uncertainty_model.num_target_qubits,
self.uncertainty_model.low, self.uncertainty_model.high,
breakpoints, slopes_delta, offsets_delta, f_min_delta, f_max_delta,
c_approx_delta)
self.european_delta = UnivariateProblem(self.uncertainty_model,
european_delta_objective)
# In[10]:
# define linear objective function
breakpoints = [0]
slopes = [1]
offsets = [0]
f_min = 0
f_max = sum(lgd)
c_approx = 0.25
objective = PwlObjective(
agg.num_sum_qubits,
0,
2**agg.num_sum_qubits -
1, # max value that can be reached by the qubit register (will not always be reached)
breakpoints,
slopes,
offsets,
f_min,
f_max,
c_approx)
# define overall multivariate problem
multivariate = MultivariateProblem(u, agg, objective)
# In[11]:
num_qubits = multivariate.num_target_qubits
num_ancillas = multivariate.required_ancillas()
q = QuantumRegister(num_qubits, name='q')
### Payoff Function
# set the strike price (should be within the low and the high value of the uncertainty)
strike_price_1 = 1.438
strike_price_2 = 2.584
# set the approximation scaling for the payoff function
c_approx = 0.25
# setup piecewise linear objective fcuntion
breakpoints = [uncertainty_model.low, strike_price_1, strike_price_2]
slopes = [0, 1, 0]
offsets = [0, 0, strike_price_2 - strike_price_1]
f_min = 0
f_max = strike_price_2 - strike_price_1
bull_spread_objective = PwlObjective(uncertainty_model.num_target_qubits,
uncertainty_model.low,
uncertainty_model.high, breakpoints,
slopes, offsets, f_min, f_max, c_approx)
# construct circuit factory for payoff function
bull_spread = UnivariateProblem(uncertainty_model, bull_spread_objective)
# plot exact payoff function (evaluated on the grid of the uncertainty model)
x = uncertainty_model.values
y = np.minimum(np.maximum(0, x - strike_price_1),
strike_price_2 - strike_price_1)
plt.plot(x, y, 'ro-')
plt.grid()
plt.title('Payoff Function', size=15)
plt.xlabel('Spot Price', size=15)
plt.ylabel('Payoff', size=15)
plt.xticks(x, size=15, rotation=90)