Lecture 10

Implementation Issues – Part 1

Overview

Choosing among the various models

Approaches for choosing parameters for the models

How to Choose Among the Various Models?

Consider the application Precision: investment bank vs. strategic

planning Security characteristics: sensitivity to term

structure model assumptions Model deficiencies and the application

Negative interest rates Perfect correlation among all rates

Tradeoff – complexity vs. accuracy

How to Choose Parameters? You’ve chosen a model (whew!) Which parameters are best? Three approaches

Judgment Statistical estimation Calibration

Statistical Estimation Analyze historical movements Given a specific interest rate model, jointly estimate all parameters

Joint estimation is difficult Chan, Karolyi, Longstaff, and Saunders

(1992, JF), Pearson and Sun (1994, JF), Amin and Morton (1994, JFE)

Model Calibration

Interest rate model should reflect existing market conditions Model prices should approximate set

of market prices Determine the best fit parameters

for alternative interest rate models Various measures of “fit”

Least sum of squared errors

Example 1: Volatility Volatility () is important for option

pricing If parameter is too low, options will be

underpriced If selling options, you will undercharge If buying options, you won’t find acceptable

prices Lesson: Consistency with other actively

traded security values Implied volatility

Example 2: Low Interest Rates Vasicek or CIR Estimate long-term mean of interest rates

to set (the mean level parameter) Value of near 8% over last 30 years

If today’s interest rate is 4.5%, what happens to asset values in a few years?

Lesson: Consistency with current economy

Example 3: Yield Spread Options

Yield spread options provide payoffs when the long-term rates exceed short-term rates by some margin (slope increases)

One-factor models (like Vasicek, CIR, Ho-Lee, BDT) all assume all yields are perfectly correlated Limits the range of the slopes

Lesson: Appropriate for application

Summary Structure of model is only half the

battle Parameter selection is challenging Consider your application Be cognizant of model limitations Scrutinize projections