  Monte Carlo (MC) simulations are widely used in financial risk management,
from estimating value-at-risk (VaR) to pricing over-the-counter derivatives.
However, they come at a significant computational cost due to the number of
scenarios required for convergence. If a probability distribution is available,
Quantum Amplitude Estimation (QAE) algorithms can provide a quadratic speed-up
in measuring its properties as compared to their classical counterparts. Recent
studies have explored the calculation of common risk measures and the
optimisation of QAE algorithms by initialising the input quantum states with
pre-computed probability distributions. If such distributions are not available
in closed form, however, they need to be generated numerically, and the
associated computational cost may limit the quantum advantage. In this paper,
we bypass this challenge by incorporating scenario generation -- i.e.
simulation of the risk factor evolution over time to generate probability
distributions -- into the quantum computation; we refer to this process as
Quantum MC (QMC) simulations. Specifically, we assemble quantum circuits that
implement stochastic models for equity (geometric Brownian motion), interest
rate (mean-reversion models), and credit (structural, reduced-form, and rating
migration credit models) risk factors. We then integrate these models with QAE
to provide end-to-end examples for both market and credit risk use cases.
