Efficient Hamiltonian Simulation for Solving Option Price Dynamics

Understand

Pricing financial derivatives, in particular European-style options at different time-maturities and strikes, means a relevant problem in finance.

• The dynamics describing the price of vanilla options when constant volatilities and interest rates are assumed, is governed by the Black-Scholes model, a linear parabolic partial differential equation with terminal value given by the pay-off of the option contract and no additional boundary conditions.
• Here, we present a digital quantum algorithm to solve Black-Scholes equation on a quantum computer by mapping it to the Schr\"odinger equation.
• The non-Hermitian nature of the resulting Hamiltonian is solved by embedding its propagator into an enlarged Hilbert space by using only one additional ancillary qubit.