Introduction to Fixed Income Analytics: Relative Value Analysis, Risk Measures, and Valuation, Second Edition

CHAPTER 17

Estimating Yield Volatility

An important input required in a valuation model is the expected interest rate volatility. We have seen how in the binomial model this parameter is required to generate the binomial interest rate tree. In the Monte Carlo model, we have seen how this parameter is required to generate the interest rate paths. In statistical analysis, the standard deviation is a measure of the variation of a random variable around its mean or expected value. Consequently, market participants use the standard deviation as a measure of volatility. In this chapter we will look at how the standard deviation of interest rates is estimated and methods for forecasting interest rate volatility.

HISTORICAL VOLATILITY

Historical volatility is the variance of a random variable using historical data and is calculated using the following formula:

(17.1)

and then

where

X_t = observation t on variable X = the sample mean for variable X T = the number of observations in the sample

Our focus is on yield volatility. More specifically, we are interested in the percentage change in daily yields. So, X_t will denote the percentage change in yield from day t and the prior day, t - 1. ...