Quantum computational finance: Monte Carlo pricing of financial derivatives

TL;DR

This paper introduces a quantum algorithm that leverages quantum superposition and amplitude estimation to perform Monte Carlo pricing of financial derivatives, achieving a quadratic speedup over classical methods.

Contribution

It presents a novel quantum algorithm for derivative pricing that combines probability distribution preparation, payoff implementation, and amplitude estimation for speedup.

Findings

Quantum superposition enables efficient probability distribution preparation.

Amplitude estimation achieves quadratic speedup in pricing accuracy.

The approach provides a foundation for quantum finance applications.

Abstract

Financial derivatives are contracts that can have a complex payoff dependent upon underlying benchmark assets. In this work, we present a quantum algorithm for the Monte Carlo pricing of financial derivatives. We show how the relevant probability distributions can be prepared in quantum superposition, the payoff functions can be implemented via quantum circuits, and the price of financial derivatives can be extracted via quantum measurements. We show how the amplitude estimation algorithm can be applied to achieve a quadratic quantum speedup in the number of steps required to obtain an estimate for the price with high confidence. This work provides a starting point for further research at the interface of quantum computing and finance.