Question

Analyze and discuss how modeling the term structure improves on the insights about yields and duration. Specifically, how does the Nelson-Siegel term structure and Nelson-Siegel-Sevensson Model determine yields inside known yield points and project the yield outside the known yields.

Answer 1

The term structure of intrest rates refers to the relationship between the yields and maturties of a set of bonds with the same credit rating. A graph of the term structure of intrest rates is known as a yeild curve.

The term structure of intrest rates for bonds or yeild curve provides insight into the future direction of intrest rates. It also reflects expectations for monetary policy conditions.

The term structure of intrest rates refers to the relationship between bonds of different terms. When intrest rates of bonds are plotted against their terms, this is called yield curve. Tbe shape of the yield curve reflects the market's future expectations for intrest rates and the conditions for monetary policy.

The two popular approaches to term structure modelling are no arbitrage models and equilibrium models. The no arbitrage tradition focusses on perfectly fitting tne term structure at a point in time to ensure that no arbitrage possibilities exist which is important for pricing derivatives. The equilibrium tradition focuses on modeling the dynamics of the instantaneous rate, typically usimg affine models after which yields at other maturities can be derived under various assumptions about the risk premium.

The model of Nelson and Siegel (1987) and its extension by Svenssom (1994) are used by central banks and other market participants as a model for the term structure of intrest rates.

Often used for developing yield curve in the practice is the NElsom Siegal model. NelsoN and siegal introduced a simple, parsimonious model wwhich can adapt to the range of yield curves:monotonic, humped and S shape.

Svensson (1994) extended Nelson Siegal model by introducing additional parameters that allow yield curve to have an addit5 hump. Thus, this model is considered to be computably more demanding

The nielson siegal model which has only four parameters enables us to estimate the yield curve, without being over parameterized, when the number of observed bond prices is limited. In the practice Nelsom-Siegal model is preferred for the use especially where there are few input data. Nelson and siegal (1987) demonstrated that their proposed model is capable of capturing many of the typically observed shapes that the spot rate curve assumes overtime. A significance weakness of the Nelson siegel model, resultinh from its low elasticity, is goodness of fit that is lower than in the case of polynomial models. When the curve is fitted to an irregular set of data points this can result in relatively large deviations of model values from actually observed rates.

The extended Nelson siegel model by Svensson offers a satisfactory precision of fit and a smooth shape of implified forwars curve. Svensson model has a number of weaknesses, e.g. a limited ability to fit irregular yield curve shapes, a tendency to take extreme values at the short end and a relatively strong co-dependence of estimates in different even non neighbouring segments of the yield curve. Thus sometimes calculations usinh Nelson siegel model can be more correct.

There are three equivalent descriptions of the term structure of intrest rates.

1. TThe discount function - which specifies zero coupon bond with a par value $1 prices as a function of maturity.

2. The spot yield curve - which specifies zero coupon bond yeilds ( spot rates) as a function of maturity.

3. The forward yield curve -which specifies zero coupon bond forward yields ( forward rates) as a fuction of maturity.