Quantum Finance

Abstract

This book applies the mathematics and concepts of quantum mechanics and quantum field theory to the modelling of interest rates and the theory of options. Particular emphasis is placed on path integrals and Hamiltonians. Financial mathematics is dominated by stochastic calculus. The present book offers a formulation that is completely independent of that approach. As such many results emerge from the ideas developed by the author. This work will be of interest to physicists and mathematicians working in the field of finance, to quantitative analysts in banks and finance firms and to practitioners in the field of fixed income securities and foreign exchange. The book can also be used as a graduate text for courses in financial physics and financial mathematics.

A Quantum-Like View to a Generalized Two Players Game

“…Hence, if what G 1 really hopes is not to get the lowest payoff 2 , he must choose 1. A similar analysis of the table from the point of view of G 2 suggests that, if also G 2 wants to avoid to get the worst 1 Notice that in any choice X 1 Y 2 the indices 1 and 2 refer to the players, while X and Y refer to the possible choices of the players, 0 or 1.…”

“…In the same way 1 1 1 2 means that both G 1 and G 2 made the same choice, "1". And so on 1 . Now, let us introduce as in [7] four real numbers a, b, c and d satisfying the inequalities c > a > d > b.…”

Value of the future: Discounting in random environments

“…To our knowledge this formalism based on Fourier analysis is not used in the economic literature of discounting, where the usual approach consists in applying the Feynman-Kac formula [26] or in the use of Fokker-Planck methods [27,28] and even quantum-field-theoretical methods [29].…”

Hamiltonian and potentials in derivative pricing models: exact results and lattice simulations

“…For barrier options it is tempting [1] to introduce a potential V (x) in order to set up a constraint on the stochastic process described by the stock price x. The corresponding generalized Hamiltonian now reads…”