Practical Guide Series in Fixed Income

The aim of the Practical Guide Series in Fixed Income is to provide non-technical and user-friendly introductions to the basic techniques used in valuation and risk analysis of fixed income securities and their derivatives.

Some of these guides are accompanied with freely downloadable Excel/VBA based software on valuation and risk analysis of fixed income securities and their derivatives. The software consists of excel spreadsheets that allow readers with basic excel skills to instantly play with the various interest rate and credit risk models. Install the software by downloading and executing the .exe file and then follow the on-screen instructions. The software requires Windows XP or later and Excel XP or later. Also, "enable" the Macros when you open the Excel files.

Submissions of practical guides in all areas of fixed income can be sent electronically as a PDF file to our contact e-mail:

Guides to Interest Rate Risk

A Practical Guide to Term Structure Estimation with Excel

The term structure of interest rates gives the relationship between the yield on an investment and the term to maturity of the investment. Since the term structure is typically measured using default-free, continuously-compounded, annualized zero-coupon yields, it is not directly observable from the published coupon bond prices and yields. This guide focuses on how to estimate the default-free term structure of interest rates from bond data using three popular methods: the bootstrapping method, the McCulloch cubic-spline method, and the Nelson and Siegel method. This guide is accompanied with free user-friendly Excel spreadsheets that allow readers with basic excel skills to instantly play with these methods for estimating the term structure of interest rates.

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Guides to Term Structure Modeling

A Practical Guide to Arbitrage-Free Pricing Using Martingales

This guide gives a practical, and easy-to-follow introduction to arbitrage-free pricing using martingales with a discrete two-period information structure. Using simple heuristic derivations, we illustrate the concepts of Arrow-Debreu prices, complete and incomplete markets, risk-neutral measure, stochastic discount factor (or pricing kernel), and Radon-Nikodym derivative. We use the discrete-time setup to give a clear and intuitive demonstration of the fundamental theorem of asset pricing, which states that absence of arbitrage is equivalent to the existence of an equivalent martingale measure under which discounted prices are martingales. We also introduce arbitrage-free pricing using martingales in continuous-time, and show the correspondence of the continuous-time results with the discrete-time results. Further, we provide two additional theorems in continuous-time, given as the Girsanov theorem and the Feynman-Kac theorem. The first theorem is used for performing a change of measure, and the second theorem is used for deriving a PDE from an expectation, and vice-versa.

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A Practical Guide to Preference-Free Vasicek and CIR Term Structure Models with Excel

This guide provides a simple introduction to the preference-free versions of the Vasicek and CIR term structure models. The preference-free versions of these models are shown to be independent of the market prices of risks, and are classified as single-plus models and double-plus models, using the new taxonomy of dynamic term structure models given by Nawalkha, Beliaeva, and Soto [2007] and Nawalkha and Soto [2008]. The accompanying excel spreadsheet file allows the user to price a number of European interest rate derivatives (such as, interest rate swaps, forward rate agreements, Eurodollar futures, Treasury futures, bond options, caps, and European interest rate swaptions), and American interest rate derivatives (such as, American bond options, and American interest rate swaptions), using single-plus (i.e., Vasicek+ and CIR+) and double-plus (Vasicek++ and CIR++) versions of these models.

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