  The financial sector is anticipated to be one of the first industries to
benefit from the increased computational power of quantum computers, in areas
such as portfolio optimisation and risk management to financial derivative
pricing. Financial mathematics, and derivative pricing in particular, are not
areas quantum physicists are traditionally trained in despite the fact that
they often have the raw technical skills needed to understand such topics. On
the other hand, most quantum algorithms have largely focused on qubits, which
are comprised of two discrete states, as the information carriers. However,
discrete higher-dimensional qudits, in addition to possibly possessing
increased noise robustness and allowing for novel error correction protocols in
certain hardware implementations, also have logarithmically greater information
storage and processing capacity. In the current NISQ era of quantum computing,
a wide array of hardware paradigms are still being studied and any potential
advantage a platform offers is worth exploring. Here we introduce the basic
concepts behind financial derivatives for the unfamiliar enthusiast as well as
outline in great detail the quantum algorithm routines needed to price a
European option, the simplest derivative. This is done within the context of a
quantum computer comprised of qudits and employing the natural
higher-dimensional analogue of a qubit-based pricing algorithm with its various
subroutines. From these pieces, one should relatively easily be able to tailor
the scheme to more complex, realistic financial derivatives. Finally, the
entire stack is numerically simulated with the results demonstrating how the
qudit-based scheme's payoff quickly approaches that of both a
similarly-resourced classical computer as well as the true payoff, within
error, for a modest increase in qudit dimension.
