A Quantum Mechanics for Interest Rate Derivatives Markets

Abstract

We present an axiomatic formulation of the Option Pricing Theory for interest rates, completely analogous to axiomatic Quantum Mechanics. The role of the wave function is played in the financial theory by discounted zero-coupon bond prices. The theory is model-free and is linked to term structure models through the Hamiltonian operator. Under the quantum framework, we prove the consistency of the Schrodinger equation with the dynamics of the stochastic string model. We also find an expression for pricing options under this quantum theory, show its consistency with standard option pricing and apply the quantum formalism to Price calls and swaptions.