A Hamiltonian Approach to Barrier Option Pricing Under Vasicek Model

TL;DR

This paper introduces a Hamiltonian method for pricing barrier options under the Vasicek interest rate model, utilizing quantum mechanics techniques to handle the time-dependent interest rate and derive pricing formulas.

Contribution

It presents a novel Hamiltonian approach combined with quantum mechanics methods for barrier option pricing under the Vasicek model, including derivation of the pricing kernel and integral formulas.

Findings

Numerical results demonstrate the method's effectiveness.

Option prices vary with underlying asset, floating rate, and regression rate.

The approach provides a new analytical framework for interest rate derivatives.

Abstract

In this paper, we study option pricing under Vasicek Model by a Hamiltonian approach. Since the interest rate changes with time, we split the time to maturity into infinite steps, and the matrix element during each step could be calculated by quantum mechanics methods. Using completeness condition, the pricing kernel and the integral expression of option price could also be derived. Numerical results of option prices as functions of underlying asset price, floating rate and regression rate are also shown.