Hamiltonian and Potentials in Derivative Pricing Models: Exact Results and Lattice Simulations

TL;DR

This paper explores quantum-inspired Hamiltonian methods and lattice simulations for pricing complex derivatives like barrier options, demonstrating their effectiveness through detailed computational strategies.

Contribution

It introduces a Hamiltonian framework combined with lattice Langevin and Monte Carlo algorithms for derivative pricing, focusing on barrier and path-dependent options.

Findings

Hamiltonian methods effectively model derivative prices.

Lattice simulations provide accurate pricing for complex options.

Computational strategies enhance simulation efficiency.

Abstract

The pricing of options, warrants and other derivative securities is one of the great success of financial economics. These financial products can be modeled and simulated using quantum mechanical instruments based on a Hamiltonian formulation. We show here some applications of these methods for various potentials, which we have simulated via lattice Langevin and Monte Carlo algorithms, to the pricing of options. We focus on barrier or path dependent options, showing in some detail the computational strategies involved.