  Quantum computers are not yet up to the task of providing computational
advantages for practical stochastic diffusion models commonly used by financial
analysts. In this paper we introduce a class of stochastic processes that are
both realistic in terms of mimicking financial market risks as well as more
amenable to potential quantum computational advantages. The type of models we
study are based on a regime switching volatility model driven by a Markov chain
with observable states. The basic model features a Geometric Brownian Motion
with drift and volatility parameters determined by the finite states of a
Markov chain. We study algorithms to estimate credit risk and option pricing on
a gate-based quantum computer. These models bring us closer to realistic market
settings, and therefore quantum computing closer the realm of practical
applications.
