Handbook of Finance: Valuation, Financial Modeling, and Quantitative Tools

Chapter 46. Pricing Options on Interest Rate Instruments

RADU TUNARU, PhD

Senior Lecturer in Financial Mathematics, City University, CASS Business School

BRIAN EALES, BA, MSc (Econ)

Academic Leader, London Metropolitan University

Abstract: Interest rate modeling has quickly become one of the main areas in financial markets. The models have grown in sophistication in response to development of new products and structures. Almost all pricing of securities and the risk management function including marking-to-market relies on interest rate modeling of some description. The information on interest rates, usually conveyed from the options markets, is important for other markets as well, such as the more established credit risk, commodities, equities, and the more recent ones such as inflation derivatives and insurance derivatives. Many models have been developed over the years, and their advantages and disadvantages should be appreciated and understood when they are applied.

Keywords: interest rates, spot rates, forward rates, interest rate modeling, short rate models, HJM framework, tree, Hull-White model, Cox-Ingersoll-Ross (CIR) models, Vasicek model, bond pricing, calibration, bond option pricing, caps

Throughout the world, interest rates serve as instruments of control. When inflation rises to an undesirable or politically unacceptable level, the appropriate authorities raise interest rates to curb expenditure. In times when economic activity and corporate and consumer confidence is less ...