The NelsonSiegelson Svensson in Python Andile Ndiweni David

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The Nelson-Siegelson. Svensson in Python ¦Andile Ndiweni ¦ David Brown ¦ Erick Mokaya ¦

The Nelson-Siegelson. Svensson in Python ¦Andile Ndiweni ¦ David Brown ¦ Erick Mokaya ¦

Our Task To select and fit some of the bootstrapped curves in Python to

Our Task To select and fit some of the bootstrapped curves in Python to the NSS Model

The term structure of interest rates This is the relationship between the yields of

The term structure of interest rates This is the relationship between the yields of default-free zerocoupon bonds and their time to maturity. The term structure is not always directly observable in the market yet it is very useful in finance. Since it cannot be observed, it needs to be estimated using approximation methods which derive the zero coupon yield or spot rate curves from observable data

Approximation Methods The Fama-Bliss bootstrapping technique –the process of extracting the zero-coupon rates from

Approximation Methods The Fama-Bliss bootstrapping technique –the process of extracting the zero-coupon rates from the coupon bearing bonds by splitting the coupons and principal of normal bonds to create virtual zero coupon bonds of longer maturity Cubic splines Exponential splines Polynomials functions Parametric methods like the Nelson-Siegel-Svensson Non-parametric methods

The Nelson. Siegel. Svensson Method The NSS model is an optimization technique used to

The Nelson. Siegel. Svensson Method The NSS model is an optimization technique used to approximate observable empirical data in order to generate yield curves. It was created by Nelson and Siegel (1987) and to include a third term by Svensson (1994) It is used by several Central banks and other market participants as a model for the term structure of interest rates. 9 out of 13 Central Banks that report their curve estimation methods Bank of International Settlements use this model. It helps to estimate the current and also to forecast the future term structure of interest rates.

The formula The Formula Where And are constants to be estimated and used to

The formula The Formula Where And are constants to be estimated and used to fit the models to the bonds university

Interpreting the terms

Interpreting the terms

Steps in computation: 1. The NSS Model We take a limited amount of bond

Steps in computation: 1. The NSS Model We take a limited amount of bond yield information, and then extrapolate and interpolate from this a good-fitting yield curve which covers all the ‘potential’ rates inbetween using the Nelson-Siegel. Svensson model. 2. We minimize the weighted sum of the squared deviations of the fitted prices from the ‘potential’ prices. We will conduct both steps first in Excel and then in Python.

The Data

The Data

The NSS Model The Excel Solver The Python Program (Find them attached)

The NSS Model The Excel Solver The Python Program (Find them attached)

Conclusion

Conclusion

Appendix Excel Sheet and 2 python code pages

Appendix Excel Sheet and 2 python code pages