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Fixed Income Modeling                         Page last updated  15/01/2009

bulletBond Pricing and Duration
bulletBond Relative Value Models
bulletTree Model for the Valuation of a Convertible Bond with Credit Risk
bulletValuing Risky Fixed and Floating Rate Debt (Longstaff & Schwartz 95)


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  1. Bond Pricing and Duration  »download


    This model allows to price a "real bond" quoted on a yield basis (which is usual for many markets, incl. New Zealand). It visualizes price as a function of yield and duration as a function of time to maturity and is mainly intended for teaching purposes.
    Note that the spreadsheet uses built-in functions PRICE, YIELD and DURATION which may not be installed on your computer. Excel can access them if you select Tools-Add-ins on your Excel menu and then tick Analysis ToolPack.

  2. Bond Relative Value Models


    Bond relative value models provide information which bonds are over-, respectively underpriced. This website presents practical Excel/VBA implementations of  some major model families. Some have been tested in practical applications in bond relative value research but they have here been adapted for academic purposes. In particular, the real time data feeds have been generalized to be independent of a particular data provider. To use them in a “real world” setting, they would require links to current price and bond data as well as utility macros to maintain the bond baskets analyzed.
    The following working paper illustrates some of the models listed below:
    Relative Value Models and Term Structure of Credit Spreads

    1. Family one are simple models based on traditional yield to maturity analysis. The yield to maturity based model shown here has two sub-components, each stored in a separate Excel workbook.

      bullet ConfBenchmark (Feb04).xls shows the implementation of a redemption yield based benchmark model for the universe of Swiss government bonds
      bullet Cheap Rich List (Feb04).xls produces a cheap/rich analysis for a universe of Swiss domestic corporate bonds using the benchmark curve generated in the Confbenchmark-model.
       
    2. The second family is the the slightly more complex JP Morgan discount function model, an approach of term-structure of interest modeling. It has been implemented for the small universe of NZD government Bonds.
       
      bullet Term structure JP Morgan Model (Feb04).xls
       
    3. The JP Morgan model was inspired by McCulloch's (1971,75) spline models that are now widely used in industry. Its limitations come to light when bond maturities in the basket are not evenly distributed on the time scale which means the fit is biased towards the concentration of bonds. McCulloch thus takes the modeling one step further by approximating the discount function through a series of cubic basis splines, fitted between so-called knot points. Literature generally recommends to set knot points such that about an equal number of bonds are in each sector. The model implementation shown here provides the choice of selecting knot points manually or automatically to have similar number of bonds in each maturity segment. The implementation is not based on the original McCulloch articles but as it was presented in Anderson et al. (1996). The sample data fitted are 81 Swiss mortgage bonds issued by the Pfandbriefbank of Swiss Cantonal Banks.
       
      bullet McCullochCubicSplineDiscountFunctionModel(P).xls
       

      References:
      McCulloch, J. H. (1971)."Measuring the Term Structure of Interest Rates". Journal of Business, 44, 19-31.
      McCulloch, J. H. (1975). "The Tax-Adjusted Yield Curve". Journal of Finance, 30, 811-829.
      Anderson, N., Breedon, F., Deacon, M., Derry, A., & Murphy, G. (1996). "Estimating and interpreting the yield curve." Chichester: John Wiley Series in Financial Economics and Quantitative Analysis. pgs. 42-44. 

       

    4. Click here to get a description of the Nelson & Siegel (1987)  yield curve fitting model
       
      bullet NelsonSiegelYieldCurveModel.xls
      bullet

      Nelson-Siegel Yield Curve Model with Svensson 1994 Extension  »download    


       

  3. Tree Model for the Valuation of a Convertible Bond with Credit Risk  »download

This is a binomial tree model adapted and extended from Hull, John C., Options, Futures & Other Derivatives. Fourth edition (2000). Prentice-Hall. P. 646f. It uses methodology formalized by K. Tsiverotis and C. Fernandes in "Valuing Convertible Bonds with credit Risk", Journal of Fixed Income, vol. 8, no. 2 (Sept 1998) pp. 95-102. For a more detailed description of this model click of  Description Tree Model for the Valuation of a Convertible Bond with Credit Risk. This description also gives the VBA code for the CB valuation function.

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Valuing Risky Fixed and Floating Rate Debt (Longstaff & Schwartz 95)  »download


In their 1995 paper F. Longstaff and Eduardo Schwartz develop a closed-form solutions for the valuation of fixed an floating rate debt subject to both credit and interest rate risk (see formulas). Summarized findings of these authors may also be found in the appendix of the following document: Relative Value Models (Feb04).pdf

While the Excel/VBA model implements both the discount bond and floating rate payment valuation, it also generates yield / maturity charts for risky fixed coupon bonds. These can be considered as a portfolio of risky discount bonds and are valued accordingly. 

As a note of caution, parameter n is used to calculate one of the terms iteratively in this model. For precise values, n would have to be set to values of 100 to 200. Yet this will slow the model, particularly the recalculation of the Excel data tables. So to gain a qualitative appreciation of parameter sensitivities, leave the value in the 10 to 20 range.

Example graph from model Parameters

 

Reference: 
 Longstaff, Francis A., Schwartz, Eduardo S. A simple approach to Valuing Risky Fixed and Floating Rate Debt. Journal of Finance. Vol 3. July 1995.

 

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Copyright © January, 2009 Kurt Hess, University of Waikato
Last modified: 13-Jan-2009