Monte-Carlo Option Pricing in Quantum Parallel

TL;DR

This paper introduces a quantum algorithm that leverages quantum parallelism to efficiently simulate asset paths and price complex financial derivatives, potentially overcoming classical computational limitations.

Contribution

The paper presents a novel quantum algorithm for derivative pricing that operates without oracles, enabling efficient high-dimensional simulations and risk analysis.

Findings

Quantum algorithm effectively simulates many asset paths in parallel.

The method accurately prices complex options and assesses portfolio risk.

Potential for improved computational efficiency over classical methods.

Abstract

Financial derivative pricing is a significant challenge in finance, involving the valuation of instruments like options based on underlying assets. While some cases have simple solutions, many require complex classical computational methods like Monte Carlo simulations and numerical techniques. However, as derivative complexities increase, these methods face limitations in computational power. Cases involving Non-Vanilla Basket pricing, American Options, and derivative portfolio risk analysis need extensive computations in higher-dimensional spaces, posing challenges for classical computers. Quantum computing presents a promising avenue by harnessing quantum superposition and entanglement, allowing the handling of high-dimensional spaces effectively. In this paper, we introduce a self-contained and all-encompassing quantum algorithm that operates without reliance on oracles or presumptions. More specifically, we develop an effective stochastic method for simulating exponentially many potential asset paths in quantum parallel, leading to a highly accurate final distribution of stock prices. Furthermore, we demonstrate how this algorithm can be extended to price more complex options and analyze risk within derivative portfolios.