English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Zendy Plus

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Zendy Tools

Zendy Open

In this paper we provide a quantum Monte Carlo algorithm to solvehigh-dimensional Black-Scholes PDEs with correlation for high-dimensionaloption pricing. The payoff function of the option is of general form and isonly required to be continuous and piece-wise affine (CPWA), which covers mostof the relevant payoff functions used in finance. We provide a rigorous erroranalysis and complexity analysis of our algorithm. In particular, we prove thatthe computational complexity of our algorithm is bounded polynomially in thespace dimension $d$ of the PDE and the reciprocal of the prescribed accuracy$\varepsilon$. Moreover, we show that for payoff functions which are bounded,our algorithm indeed has a speed-up compared to classical Monte Carlo methods.Furthermore, we provide numerical simulations in one and two dimensions usingour developed package within the Qiskit framework tailored to price CPWAoptions with respect to the Black-Scholes model, as well as discuss thepotential extension of the numerical simulations to arbitrary space dimension.

Quantum Monte Carlo algorithm for solving Black-Scholes PDEs for high-dimensional option pricing in finance and its complexity analysis