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Lecture 10

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

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Lecture 10

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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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