Computing the Payoff Function of a European Option Using Quantum Amplitude Estimation

The present work focuses on the evaluation of the Quantum Amplitude Estimation method for the valuation of European options as an alternative method to classical methods by implementing the Quantum Pricing Method using CPU, GPU, and QPU (Quantum Processing Units); solving the Black-Scholes equation and using its solution as the reference method; implementing Monte Carlo and Binomial numerical methods for option valuation; and comparing the different methods in terms of accuracy, computational complexity, and applicability. To estimate the options, Python was employed to solve the Black-Scholes equation , the Binomial model, Monte Carlo simulations, and Qiskit for the Quantum Amplitude Estimation method in the IBM Quantum Platform . Classical numerical methods were implemented on CPU, while simulations of the quantum method used CPU, GPU, and QPU obtaining different results in terms of computation time and accuracy. The main results show the convergence of the models and the scaling of computation times concerning the number of iterations. Additionally, results on computational efficiency are presented, where classical methods are useful for common applications by accessibility and fast implementation. Although the Quantum Method requires large computation time, it uses few resources to reach the solution . Moreover, its implementation involves the use of quantum circuits, which presents a new way to approach algorithms that need further study. The Quantum Method shows a more efficient use of resources and opens new perspectives in solving financial problems through new methods of this evolving technology.