Quantum Advantage for Multi-option Portfolio Pricing and Valuation Adjustments

TL;DR

This paper develops quantum algorithms to efficiently estimate credit valuation adjustments and multi-option portfolio prices, potentially reducing computational complexity in financial risk management.

Contribution

It introduces quantum Monte Carlo methods combined with amplitude estimation for faster, more accurate financial risk calculations involving complex derivatives.

Findings

Quantum algorithms improve sampling efficiency for CVA and portfolio pricing.

Application of quantum Monte Carlo techniques under known variance bounds.

Analysis of conditions for effective quantum algorithm deployment.

Abstract

A critical problem in the financial world deals with the management of risk, from regulatory risk to portfolio risk. Many such problems involve the analysis of securities modelled by complex dynamics that cannot be captured analytically, and hence rely on numerical techniques that simulate the stochastic nature of the underlying variables. These techniques may be computationally difficult or demanding. Hence, improving these methods offers a variety of opportunities for quantum algorithms. In this work, we study the problem of Credit Valuation Adjustments (CVAs) which has significant importance in the valuation of derivative portfolios. As a variant, we also consider the problem of pricing a portfolio of many different financial options. We propose quantum algorithms that accelerate statistical sampling processes to approximate the price of the multi-option portfolio and the CVA under different measures of dispersion. Technically, our algorithms are based on enhancing the quantum Monte Carlo (QMC) algorithms by Montanaro with an unbiased version of quantum amplitude estimation. We analyse the conditions under which we may employ these techniques and demonstrate the application of QMC techniques on CVA approximation when particular bounds for the variance of CVA are known.