FixedIncomePricingObjective

class FixedIncomePricingObjective(num_qubits, pca_matrix, initial_interests, cash_flow, rescaling_factor, bounds)

Bases: QuantumCircuit

The Fixed Income Expected Value amplitude function. This circuit can be used to evaluate the expected value of the total value $V$ of the assets

$$V=\sum _{t=1}^T\frac{c_t}{(1+r_t{)}^t}.$$

Here $c_t$ are the cash flows of the assets and $r_t$ are the interest rates. The interest rates are subject to uncertainty and can be described by a PCA-decomposition into the pca_matrix $A$ and initial_interests $\overrightarrow{b}$. For a sample $\overrightarrow{x}$ of a random variable, the interest rates are modeled as:

$$\overrightarrow{r}=A\overrightarrow{x}+\overrightarrow{b}.$$

The number of qubits used to represent each asset is specified by num_qubits and the bounds of the random variable by bounds. The approximation of the objective function follows [1]. .. rubric:: References

[1]: Woerner, S., & Egger, D. J. (2018).

Quantum Risk Analysis. arXiv:1806.06893

Parameters:

• num_qubits (List[int]) – A list specifying the number of qubits used to discretize the assets.

• pca_matrix (ndarray) – The PCA matrix for the changes in the interest rates, ${\delta }_r$.

• initial_interests (List[int]) – The initial interest rates / offsets for the interest rates.

• cash_flow (List[float]) – The cash flow time series.

• rescaling_factor (float) – The scaling factor used in the Taylor approximation.

• bounds (List[Tuple[float, float]]) – The list of the tuple of the bounds, (min, max), for return values the assets can attain.

Attributes

Methods

post_processing(scaled_value)

Map the scaled value back to the original domain. :param scaled_value: The scaled value.

Returns:

The scaled value mapped back to the original domain.

Return type:

float