Module 17 - Linking Models, Parameters, Library Package and Updates.pdf
Lecture 10 Implementation Issues – Part 1 Overview Choosing among the various models Approaches...
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Transcript of Lecture 10 Implementation Issues – Part 1 Overview Choosing among the various models Approaches...
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