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

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

2002-11-21

arxiv.org/abs/cond-mat/0211489v2

PhysicaA334:531-557,2004

Physics

Condensed Matter

Soft Condensed Matter

27 pages, 11 figures 1 subsection added (4.1). Slightly longer appendix

Scientific paper

10.1016/j.physa.2003.10.080

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.

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