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Implementation Issues in Choosing Models and Parameters for Interest Rate Modeling

Learn about the challenges and considerations in selecting appropriate models and parameters for interest rate modeling, including precision, security characteristics, model deficiencies, and the tradeoff between complexity and accuracy.

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Implementation Issues in Choosing Models and Parameters for Interest Rate Modeling

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  1. Lecture 10 Implementation Issues – Part 1

  2. Overview • Choosing among the various models • Approaches for choosing parameters for the models

  3. 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

  4. How to Choose Parameters? • You’ve chosen a model (whew!) • Which parameters are best? • Three approaches • Judgment • Statistical estimation • Calibration

  5. 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)

  6. 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

  7. Example 1: Volatility • Volatility (s) 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

  8. Example 2: Low Interest Rates • Vasicek or CIR • Estimate long-term mean of interest rates to set q (the mean level parameter) • Value of q 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

  9. 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

  10. Summary • Structure of model is only half the battle • Parameter selection is challenging • Consider your application • Be cognizant of model limitations • Scrutinize projections

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