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

Chapter 22. The Concept and Measures of Interest Rate Volatility

ALEXANDER LEVIN, PhD

Director of Valuation Modeling, Andrew Davidson and Co., Inc.

Abstract: The knowledge of interest rates and cash flows represents the basis for valuation of fixed income financial instruments. In reality, not only are future interest rates random, but also the future cash flows of many securitized investments are also uncertain, as they depend (are "contingent") on interest rates. Valuation of rate options and embedded option bonds, including MBS and ABS, requires sophisticated models of this randomness.

Keywords: daily increments, short rate, long rates, Brownian motion, diffusion, jumps, Poisson events, volatility, drift, mean reversion, stochastic differential equation

In this chapter, we introduce the concepts of market volatility and discuss how it is measured. The dynamics of rates are subject to market forces, mean reversion, and combination of diffusions and jumps.

BASIC DEFINITIONS AND FIRST FINDINGS

We can't tell in advance what interest rates will be. Investors may be either enriched or bankrupted from sudden changes in interest rates. Financial institutions devote considerable resources to risk management and hedging. Yet, if future interest rates were deterministic, there would be no need to hedge. Coping with uncertainty is a central feature of investment markets.

The pricing of options and embedded-options instruments utilizes a statistical concept to describe the magnitude of potential ...