Quantum algorithms for computational finance applications

Recently there has been increased interest on quantum algorithms and how they are applied to real life problems. But is this interest justified? As an example, researchers have tried to apply quantum algorithms to solve linear systems of equations faster. These algorithms are considered to be more efficient and perform better than classical algorithms, in general. Among other fields, the field of finance presents real life problems, such as portfolio optimization and options pricing, which may exploit the efficiency of quantum algorithms for their solution. The purpose of this thesis is to apply both classical and quantum algorithms in two important financial problems namely portfolio optimization and options pricing. We utilize advanced quantum algorithms such as the Variational Quantum Eigensolver (VQE) and the Quantum Amplitude Estimation (QAE). VQE is a hybrid classical-quantum algorithm that is applied for optimization problems e.g. molecule simulations, and optimization problems. In this thesis I am applying the VQE algorithm to solve linear systems of equations in the framework of the Markowitz portfolio optimization model. QAE is a method used in quantum computing to measure probabilities of desired states and is a generalization of Grover’s search algorithm. I apply QAE to options pricing and I compare it to the classical Black-Scholes Merton model for pricing European call and put options. I have used IBM’s Quantum Experience platform to run the software developed and compare the performance of the aforementioned quantum and classical algorithms.Recently there has been increased interest on quantum algorithms and how they are applied to real life problems. But is this interest justified? As an example, researchers have tried to apply quantum algorithms to solve linear systems of equations faster. These algorithms are considered to be more efficient and perform better than classical algorithms, in general. Among other fields, the field of finance presents real life problems, such as portfolio optimization and options pricing, which may exploit the efficiency of quantum algorithms for their solution. The purpose of this thesis is to apply both classical and quantum algorithms in two important financial problems namely portfolio optimization and options pricing. We utilize advanced quantum algorithms such as the Variational Quantum Eigensolver (VQE) and the Quantum Amplitude Estimation (QAE). VQE is a hybrid classical-quantum algorithm that is applied for optimization problems e.g. molecule simulations, and optimization problems. In this thesis I am applying the VQE algorithm to solve linear systems of equations in the framework of the Markowitz portfolio optimization model. QAE is a method used in quantum computing to measure probabilities of desired states and is a generalization of Grover’s search algorithm. I apply QAE to options pricing and I compare it to the classical Black-Scholes Merton model for pricing European call and put options. I have used IBM’s Quantum Experience platform to run the software developed and compare the performance of the aforementioned quantum and classical algorithms