Solving Black Scholes PDE with a quantum computer [QCT20/21, Seminar #02]

By Javier González Conde (Quantum Mads).


A fundamental task of quantitative finance is calculating the fair price for options, derivative contracts that give the holder the right to buy or sell an underlying asset on a specified date and strike price. The first successful approach to this problem was Black-Scholes model. Although an analytical solution exists, numerical methods are extensively analyzed to solve this model, serving as the ground for more complex models. It has been tackled stochastically employing a quantum Monte Carlo method with quadratic speedup implemented in the IBM computers and also using an unary representation of the asset value.

Javier González presents a digital quantum algorithm with exponential speed-up to solve the partial differential equation of the model in the case of vanilla options, showing a feasible approach to price financial derivatives on a digital quantum computer by Hamiltonian simulation techniques. The protocol introduced can be easily extended to include additional degrees of freedom, e.g. time dependent volatility or coupled options.

Javier González Conde is the CEO of Quantum Mads, a Spanish startup focused on the applications of Quantum Computing for the financial services industry. His team aims to dissect the intrinsic dynamics of complex financial systems, creating QC-based solutions that will disrupt the current state of the art. Javier completed a double degree in Physics and Mathematics in Universidad Complutense de Madrid (UCM), and pursued a master's degree in Big Data jointly taught by UCM and Universidad Politécnica de Madrid, while applying his knowledge to different businesses in Accenture Digital. Apart from his role as CEO, he participates in Universidad del País Vasco as predoctoral researcher.

Webinar hosted by Universidad Politécnica de Madrid, as part of its Master in Quantum Computing Technology (https://www.quantum-explore.com)