Estimating the Term-Structure

In our theoretical framework we often assume a term-structure for the continuum of maturities T. In other words, we assume that the forward or zero-coupon yield curve is given by a function of the continuous variable T. This should be seen as approximation of the reality, which comes along with finitely many (possibly noisy) market quote observations. In Chap. 11 we will model the term-structure of interest rates by choosing finitely many maturities. This is appropriate if we want to price a predetermined finite set of derivatives, such as caps and swaptions. However, as soon as more exotic derivatives be priced whose cash flow dates possibly do not match the predetermined finite time grid, one has to interpolate the term-structure. In this chapter, we learn some term-structure estimation methods. We start with a bootstrapping example, which is the most used method among the trading desks. We then consider more general aspects of non-parametric and parametric term-structure estimation methods. In the last part we perform a principal component analysis for the term-structure movements, which is the best-known dimension reduction technique in multivariate data analysis.