| Περίληψη |
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.
|
Quantum algorithms for computational finance applications
