Vineet Virmani

On estimability of parsimonious term structure models: an experiment with the Nelson–Siegel specification

This study addresses operational issues in estimation of parsimonious term structure models. When using price errors, objective function in term structure estimation is a nonlinear function of the model parameters. This necessarily entails using numerical optimization techniques for estimation, which brings to fore the issue of (sensitivity of final results to) the choice of initialization of the optimization routine. This study assesses the sensitivity of the final objective function value and the final parameter vector to the choice of the ‘initial guess’ during the estimation of the popular Nelson–Siegel model. It turns out that there exist regions in the shape of the objective function where a slight change in (seemingly reasonable) initial vector takes one far from optimum. Choice of the (range of) ‘best’ starting vector turns out to be an empirical matter. Grid search is recommended. One must first get to a subset of initial values that results in the objective function value near a minimum and then assess the sensitivity of the final parameter vector to those relevant (subset of) initial values. The study illustrates the process using a typical trading days data.

Computational Finance Using QuantLib-Python

Given the complexity of over-the-counter derivatives and structured products, almost all derivatives pricing today is based on numerical methods. Large financial institutions typically have their own teams of developers who maintain state-of-the-art financial libraries, but until a few years ago, none of that sophistication was available for use in teaching and research. However, for the past decade, QuantLib, a reliable C++ open source library, has been available. In this article, the authors introduce QuantLib for pricing derivatives and document their experiences using its Python extension, QuantLib-Python, in their computational finance course at the Indian Institute of Management, Ahmedabad. The fact that QuantLib is available in Python makes it possible to harness the power of C++ with the ease of IPython notebooks for use in both the classroom and student projects.

Distribution of Cross-Section of Price Changes and Measurement of Inflation

In this study we look at the statistical properties of components forming the Wholesale Price Index (WPI), the headline inflation index for the Indian economy. We find that not only is the distribution of price changes at the disaggregate level highly leptokurtic, but also the cross-sectional distribution of price changes is positively skewed. This has the implication that the weighted mean would fail to be an efficient estimator of inflation. Trimmed Means, belonging to the class of limited influence estimators, have been used by many central banks to get around the skewness problem. We also explore the use of trimmed means for efficiently estimating inflation for India. In particular, we study the robustness of trimmed means to the benchmark (Centered Moving Average vs. trends derived from the Hodrick Prescott Filter) and the evaluation criteria (Mean Absolute Deviation vs. Root Mean Square Error vs. an Asymmetric Loss Function). Although we study the performance of trimmed means against the weighted mean in some detail, we stop short of proposing any ‘one’ trimming pattern as the ideal. The selection of the headline inflation rate depends as much on its ability to track the underlying trend void of transitory disturbances as much on its ability to forecast future inflation and its correlation with money growth, something we don’t deal with in the present study.