Quantum Theory for the Binomial Model in Finance Theory

Abstract

In this paper, a quantum model for the binomial market in finance is proposed. We show that its risk-neutral world exhibits an intriguing structure as a disk in the unit ball of ${\mathbf{R}}^3,$ whose radius is a function of the risk-free interest rate with two thresholds which prevent arbitrage opportunities from this quantum market. Furthermore, from the quantum mechanical point of view we re-deduce the Cox-Ross-Rubinstein binomial option pricing formula by considering Maxwell-Boltzmann statistics of the system of $N$ distinguishable particles.

Latex, 8 pages,1 figure, revised version,submitted

References in corpus (1)

• Quantum Finance: The Finite Dimensional Case

Cited by in corpus (3)

• Quantum Finance: The Finite Dimensional Case
• A Non-commutative Version of the Fundamental Theorem of Asset Pricing
• On the quantum behavior and clustering properties of correlated financial portfolios