class EuropeanCallExpectedValue(UncertaintyProblem):
"""
The European Call Option Expected Value.
Evaluates the expected payoff for a European call option given an uncertainty model.
The payoff function is f(S, K) = max(0, S - K) for a spot price S and strike price K.
"""
def __init__(self,
uncertainty_model: UnivariateDistribution,
strike_price: float,
c_approx: float,
i_state: Optional[Union[List[int], np.ndarray]] = None,
i_compare: Optional[int] = None,
i_objective: Optional[int] = None) -> None:
"""
Constructor.
Args:
uncertainty_model: uncertainty model for spot price
strike_price: strike price of the European option
c_approx: approximation factor for linear payoff
i_state: indices of qubits representing the uncertainty
i_compare: index of qubit for comparing spot price to strike price
(enabling payoff or not)
i_objective: index of qubit for objective function
"""
super().__init__(uncertainty_model.num_target_qubits + 2)
self._uncertainty_model = uncertainty_model
self._strike_price = strike_price
self._c_approx = c_approx
if i_state is None:
i_state = list(range(uncertainty_model.num_target_qubits))
self.i_state = i_state
if i_compare is None:
i_compare = uncertainty_model.num_target_qubits
self.i_compare = i_compare
if i_objective is None:
i_objective = uncertainty_model.num_target_qubits + 1
self.i_objective = i_objective
# map strike price to {0, ..., 2^n-1}
lb = uncertainty_model.low
ub = uncertainty_model.high
self._mapped_strike_price = int(np.round((strike_price - lb) /
(ub - lb) * (uncertainty_model.num_values - 1)))
# create comparator
self._comparator = FixedValueComparator(uncertainty_model.num_target_qubits,
self._mapped_strike_price)
self.offset_angle_zero = np.pi / 4 * (1 - self._c_approx)
if self._mapped_strike_price < uncertainty_model.num_values - 1:
self.offset_angle = -1 * np.pi / 2 * self._c_approx * self._mapped_strike_price / \
(uncertainty_model.num_values - self._mapped_strike_price - 1)
self.slope_angle = np.pi / 2 * self._c_approx / \
(uncertainty_model.num_values - self._mapped_strike_price - 1)
else:
self.offset_angle = 0
self.slope_angle = 0
def value_to_estimation(self, value):
estimator = value - 1 / 2 + np.pi / 4 * self._c_approx
estimator *= 2 / np.pi / self._c_approx
estimator *= (self._uncertainty_model.num_values - self._mapped_strike_price - 1)
estimator *= (self._uncertainty_model.high - self._uncertainty_model.low) / \
(self._uncertainty_model.num_values - 1)
return estimator
def required_ancillas(self):
num_uncertainty_ancillas = self._uncertainty_model.required_ancillas()
num_comparator_ancillas = self._comparator.required_ancillas()
num_ancillas = int(np.maximum(num_uncertainty_ancillas, num_comparator_ancillas))
return num_ancillas
def build(self, qc, q, q_ancillas=None, params=None):
# get qubits
q_state = [q[i] for i in self.i_state]
q_compare = q[self.i_compare]
q_objective = q[self.i_objective]
# apply uncertainty model
self._uncertainty_model.build(qc, q_state, q_ancillas)
# apply comparator to compare qubit
self._comparator.build(qc, q_state + [q_compare], q_ancillas)
# apply approximate payoff function
qc.ry(2 * self.offset_angle_zero, q_objective)
qc.cry(2 * self.offset_angle, q_compare, q_objective)
for i, qi in enumerate(q_state):
qc.mcry(2 * self.slope_angle * 2 ** i, [q_compare, qi], q_objective, None)
class EuropeanCallDelta(UncertaintyProblem):
"""
The European Call Option Delta.
Evaluates the variance for a European call option given an uncertainty model.
The payoff function is f(S, K) = max(0, S - K) for a spot price S and strike price K.
"""
CONFIGURATION = {
'name':
'EuropeanCallDelta',
'description':
'European Call Delta',
'input_schema': {
'$schema': 'http://json-schema.org/schema#',
'id': 'ECD_schema',
'type': 'object',
'properties': {
'strike_price': {
'type': 'number',
'default': 0
},
'i_state': {
'type': ['array', 'null'],
'items': {
'type': 'integer'
},
'default': None
},
'i_objective': {
'type': ['integer', 'null'],
'default': None
}
},
'additionalProperties': False
},
'depends': [
{
'pluggable_type': 'univariate_distribution',
'default': {
'name': 'NormalDistribution'
}
},
],
}
def __init__(self,
uncertainty_model,
strike_price,
i_state=None,
i_objective=None):
"""
Constructor.
Args:
uncertainty_model (UnivariateDistribution): uncertainty model for spot price
strike_price (float): strike price of the European option
c_approx (float): approximation factor for linear payoff
i_state (list or array): indices of qubits representing the uncertainty
i_objective (int): index of qubit for objective function
"""
super().__init__(uncertainty_model.num_target_qubits + 1)
self._uncertainty_model = uncertainty_model
self._strike_price = strike_price
if i_state is None:
i_state = list(range(uncertainty_model.num_target_qubits))
self.i_state = i_state
if i_objective is None:
i_objective = uncertainty_model.num_target_qubits
self.i_objective = i_objective
super().validate(locals())
# map strike price to {0, ..., 2^n-1}
lb = uncertainty_model.low
ub = uncertainty_model.high
self._mapped_strike_price = int(
np.ceil((strike_price - lb) / (ub - lb) *
(uncertainty_model.num_values - 1)))
# create comparator
self._comparator = FixedValueComparator(
uncertainty_model.num_target_qubits, self._mapped_strike_price)
def required_ancillas(self):
num_uncertainty_ancillas = self._uncertainty_model.required_ancillas()
num_comparator_ancillas = self._comparator.required_ancillas()
num_ancillas = num_uncertainty_ancillas + num_comparator_ancillas
return num_ancillas
def required_ancillas_controlled(self):
num_uncertainty_ancillas = self._uncertainty_model.required_ancillas_controlled(
)
num_comparator_ancillas = self._comparator.required_ancillas_controlled(
)
num_ancillas_controlled = num_uncertainty_ancillas + num_comparator_ancillas
return num_ancillas_controlled
def build(self, qc, q, q_ancillas=None):
# get qubit lists
q_state = [q[i] for i in self.i_state]
q_objective = q[self.i_objective]
# apply uncertainty model
self._uncertainty_model.build(qc, q_state, q_ancillas)
# apply comparator to compare qubit
self._comparator.build(qc, q_state + [q_objective], q_ancillas)
class EuropeanCallExpectedValue(UncertaintyProblem):
"""
The European Call Option Expected Value.
Evaluates the expected payoff for a European call option given an uncertainty model.
The payoff function is f(S, K) = max(0, S - K) for a spot price S and strike price K.
"""
CONFIGURATION = {
'name':
'EuropeanCallExpectedValue',
'description':
'European Call Expected Value',
'input_schema': {
'$schema': 'http://json-schema.org/draft-07/schema#',
'id': 'ECEV_schema',
'type': 'object',
'properties': {
'strike_price': {
'type': 'number',
'default': 0
},
'c_approx': {
'type': 'number',
'default': 0.5
},
'i_state': {
'type': ['array', 'null'],
'items': {
'type': 'integer'
},
'default': None
},
'i_compare': {
'type': ['integer', 'null'],
'default': None
},
'i_objective': {
'type': ['integer', 'null'],
'default': None
}
},
'additionalProperties': False
},
'depends': [
{
'pluggable_type': 'univariate_distribution',
'default': {
'name': 'NormalDistribution'
}
},
],
}
def __init__(self,
uncertainty_model,
strike_price,
c_approx,
i_state=None,
i_compare=None,
i_objective=None):
"""
Constructor.
Args:
uncertainty_model (UnivariateDistribution): uncertainty model for spot price
strike_price (float): strike price of the European option
c_approx (float): approximation factor for linear payoff
i_state (list or array): indices of qubits representing the uncertainty
i_compare (int): index of qubit for comparing spot price to strike price
(enabling payoff or not)
i_objective (int): index of qubit for objective function
"""
super().__init__(uncertainty_model.num_target_qubits + 2)
self._uncertainty_model = uncertainty_model
self._strike_price = strike_price
self._c_approx = c_approx
if i_state is None:
i_state = list(range(uncertainty_model.num_target_qubits))
self.i_state = i_state
if i_compare is None:
i_compare = uncertainty_model.num_target_qubits
self.i_compare = i_compare
if i_objective is None:
i_objective = uncertainty_model.num_target_qubits + 1
self.i_objective = i_objective
super().validate(locals())
# map strike price to {0, ..., 2^n-1}
lb = uncertainty_model.low
ub = uncertainty_model.high
self._mapped_strike_price = int(
np.round((strike_price - lb) / (ub - lb) *
(uncertainty_model.num_values - 1)))
# create comparator
self._comparator = FixedValueComparator(
uncertainty_model.num_target_qubits, self._mapped_strike_price)
self.offset_angle_zero = np.pi / 4 * (1 - self._c_approx)
if self._mapped_strike_price < uncertainty_model.num_values - 1:
self.offset_angle = -1 * np.pi / 2 * self._c_approx * self._mapped_strike_price / \
(uncertainty_model.num_values - self._mapped_strike_price - 1)
self.slope_angle = np.pi / 2 * self._c_approx / \
(uncertainty_model.num_values - self._mapped_strike_price - 1)
else:
self.offset_angle = 0
self.slope_angle = 0
def value_to_estimation(self, value):
estimator = value - 1 / 2 + np.pi / 4 * self._c_approx
estimator *= 2 / np.pi / self._c_approx
estimator *= (self._uncertainty_model.num_values -
self._mapped_strike_price - 1)
estimator *= (self._uncertainty_model.high - self._uncertainty_model.low) / \
(self._uncertainty_model.num_values - 1)
return estimator
def required_ancillas(self):
num_uncertainty_ancillas = self._uncertainty_model.required_ancillas()
num_comparator_ancillas = self._comparator.required_ancillas()
num_ancillas = int(
np.maximum(num_uncertainty_ancillas, num_comparator_ancillas))
return num_ancillas
def build(self, qc, q, q_ancillas=None, params=None):
# get qubits
q_state = [q[i] for i in self.i_state]
q_compare = q[self.i_compare]
q_objective = q[self.i_objective]
# apply uncertainty model
self._uncertainty_model.build(qc, q_state, q_ancillas)
# apply comparator to compare qubit
self._comparator.build(qc, q_state + [q_compare], q_ancillas)
# apply approximate payoff function
qc.ry(2 * self.offset_angle_zero, q_objective)
qc.cry(2 * self.offset_angle, q_compare, q_objective)
for i, qi in enumerate(q_state):
qc.mcry(2 * self.slope_angle * 2**i, [q_compare, qi], q_objective,
None)
class EuropeanCallDelta(UncertaintyProblem):
"""
The European Call Option Delta.
Evaluates the variance for a European call option given an uncertainty model.
The payoff function is f(S, K) = max(0, S - K) for a spot price S and strike price K.
"""
def __init__(self,
uncertainty_model: UnivariateDistribution,
strike_price: float,
i_state: Optional[Union[List[int], np.ndarray]] = None,
i_objective: Optional[int] = None) -> None:
"""
Constructor.
Args:
uncertainty_model: uncertainty model for spot price
strike_price: strike price of the European option
i_state: indices of qubits representing the uncertainty
i_objective: index of qubit for objective function
"""
super().__init__(uncertainty_model.num_target_qubits + 1)
self._uncertainty_model = uncertainty_model
self._strike_price = strike_price
if i_state is None:
i_state = list(range(uncertainty_model.num_target_qubits))
self.i_state = i_state
if i_objective is None:
i_objective = uncertainty_model.num_target_qubits
self.i_objective = i_objective
# map strike price to {0, ..., 2^n-1}
lb = uncertainty_model.low
ub = uncertainty_model.high
self._mapped_strike_price = int(
np.ceil((strike_price - lb) / (ub - lb) *
(uncertainty_model.num_values - 1)))
# create comparator
self._comparator = FixedValueComparator(
uncertainty_model.num_target_qubits, self._mapped_strike_price)
def required_ancillas(self):
num_uncertainty_ancillas = self._uncertainty_model.required_ancillas()
num_comparator_ancillas = self._comparator.required_ancillas()
num_ancillas = num_uncertainty_ancillas + num_comparator_ancillas
return num_ancillas
def required_ancillas_controlled(self):
num_uncertainty_ancillas = self._uncertainty_model.required_ancillas_controlled(
)
num_comparator_ancillas = self._comparator.required_ancillas_controlled(
)
num_ancillas_controlled = num_uncertainty_ancillas + num_comparator_ancillas
return num_ancillas_controlled
def build(self, qc, q, q_ancillas=None, params=None):
# get qubit lists
q_state = [q[i] for i in self.i_state]
q_objective = q[self.i_objective]
# apply uncertainty model
self._uncertainty_model.build(qc, q_state, q_ancillas)
# apply comparator to compare qubit
self._comparator.build(qc, q_state + [q_objective], q_ancillas)