# -*- coding: utf-8 -*-
# This code is part of Qiskit.
#
# (C) Copyright IBM 2018, 2020.
#
# This code is licensed under the Apache License, Version 2.0. You may
# obtain a copy of this license in the LICENSE.txt file in the root directory
# of this source tree or at http://www.apache.org/licenses/LICENSE-2.0.
#
# Any modifications or derivative works of this code must retain this
# copyright notice, and modified files need to carry a notice indicating
# that they have been altered from the originals.
"""The European Call Option Expected Value."""
from typing import Optional, Union, List
import numpy as np
from qiskit.circuit.library import IntegerComparator
from qiskit.aqua.components.uncertainty_models import UnivariateDistribution
from qiskit.aqua.components.uncertainty_problems import UncertaintyProblem
[docs]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}
lower = uncertainty_model.low
upper = uncertainty_model.high
self._mapped_strike_price = int(np.round((strike_price - lower) /
(upper - lower) *
(uncertainty_model.num_values - 1)))
# create comparator
self._comparator = IntegerComparator(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
[docs] 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
[docs] def required_ancillas(self):
num_uncertainty_ancillas = self._uncertainty_model.required_ancillas()
num_comparator_ancillas = self._comparator.num_ancilla_qubits
num_ancillas = int(np.maximum(num_uncertainty_ancillas, num_comparator_ancillas))
return num_ancillas
[docs] 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
qubits = q_state[:] + [q_compare]
if q_ancillas:
qubits += q_ancillas[:self._comparator.num_ancilla_qubits]
qc.append(self._comparator.to_instruction(), qubits)
# 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, q_i in enumerate(q_state):
qc.mcry(2 * self.slope_angle * 2 ** i, [q_compare, q_i], q_objective, None)