Physica A 401 (2014) 182–200 Contents lists available at ScienceDirect Physica A journal homepage: www.elsevier.com/locate/physa Pricing of range accrual swap in the quantum finance Libor Market Model Belal E. Baaquie a,b , Xin Du a,∗ , Pan Tang c , Yang Cao a a Department of Physics, National University of Singapore, 2 Science Drive 3, Singapore 117542, Singapore b Risk Management Institute, National University of Singapore, Singapore c Department of Finance, School of Economics and Management, Southeast University, Nanjing, Jiangsu 210096, China highlights • The range accrual swap is modelled in the framework of Quantum Finance and the approximate price is obtained using an expansion in the Libor volatility. • The price of accrual swap is numerically analysed by generating daily sample values of a two dimension Gaussian quantum field. • The Monte Carlo simulation method is used to study the nonlinear domain of the model and determine the range of validity of the approximate formula. article info Article history: Received 27 September 2013 Received in revised form 12 November 2013 Available online 28 January 2014 Keywords: Quantum finance Range accrual swap Monte Carlo simulation abstract We study the range accrual swap in the quantum finance formulation of the Libor Market Model (LMM). It is shown that the formulation can exactly price the path dependent instrument. An approximate price is obtained as an expansion in the volatility of Libor. The Monte Carlo simulation method is used to study the nonlinear domain of the model and determine the range of validity of the approximate formula. The price of accrual swap is analyzed by generating daily sample values by simulating a two dimension Gaussian quantum field. Crown Copyright © 2014 Published by Elsevier B.V. All rights reserved. 1. Introduction Range accrual swap is a type of a derivative product that is similar to normal interest rate swap. The investor may have a view that the market is or is not very volatile and that consequently some index will or will not stay within a predefined range. The range accrual index could be an interest rate, an FX rate or a commodity price. The investor makes an additional profit if the view taken is correct and loses money otherwise. The range accrual can also serve to hedge risks since the payments are based on daily observations and not on a pre-fixed rate. The interest range accrual swap is one of the most popular non-vanilla interest rate derivatives; more than USD 160 billion of range accrual indexed on interest rates have been sold since 2004, and the total volumes have been increasing rapidly in the last few years. The present work investigates the range accrual swap based on the behavior of the 3-month Libor. The range accrual for interest rates has been studied in many books and articles, such as Navatte and Quittard-Pinon [1], Nunes [2] using the Gaussian HJM (Heath–Jarrow–Morton) framework, Damiano Brigo and Fabio Mercurio using the BGM- ∗ Corresponding author. Tel.: +65 96458390. E-mail addresses: phybeb@nus.edu.sg (B.E. Baaquie), duxin.nus@gmail.com (X. Du), pantangnus@gmail.com (P. Tang), yangcao@nus.edu.sg (Y. Cao). 0378-4371/$ – see front matter Crown Copyright © 2014 Published by Elsevier B.V. All rights reserved. http://dx.doi.org/10.1016/j.physa.2014.01.042