A Quantum Mechanics for interest rate derivatives markets. (February 2022)

• Record Type: Journal Article
• Authors: Bueno-Guerrero, Alberto
• Is Part Of: Chaos, solitons and fractals. Volume 155(2022)
• Publication Date: 2022-02
• Subjects: Quantum mechanics -- Hamiltonian operator -- Schrödinger equation -- Option pricing -- Perturbation theory; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2021.111726
• Languages: English
• ISSNs: 0960-0779

Abstract

Highlights: We reformulate the axioms of Quantum Mechanics to price interest rate derivatives. The resulting framework is equivalent to standard Option Pricing Theory. The new model is linked with term structure models through the Hamiltonian operator. We develop a time-dependent perturbation theory for the financial framework. We apply it to a call under the HW model with a small local volatility perturbation. Abstract: We present a model-free axiomatic formulation of Option Pricing Theory for interest rate derivatives. In this setting, completely analogous to axiomatic Quantum Mechanics, the role of the wave function is played by the discounted zero-coupon bond price. The theory is linked to term structure models through the Hamiltonian operator, and we show that its associated Schrödinger equation is consistent with the [25] model. We also find the quantum-mechanical equivalent of the standard risk-neutral option pricing formula. In order to take advantage of this quantum framework, we develop a time-dependent perturbation theory and we apply it to obtain an approximate closed-form expression for the price of a call option under the [26] model with a small local volatility perturbation.