Corporate Bond Yield Curve

Question

I am an intern in a mutual fund and they have asked me to create in house yield curve for different type bonds in their portfolio

I need to know on what basis are different yield curves made. For example GSec Yield curves are different from corporate ones and Corporate ones are differentiated by ratings and all of them use different fitting curves . E.g Nelson-Siegel or cubic splines.

Can anyone give me a concise classification of what fitting method to use for different type of bonds(AAA, B etc) or link me to a documentation for the same

Answer 1

Creating yield curves:

1. Pick one fitting method and use it throughout e.g. a cubic spline interpolation
2. Determine an approach that allocates bond securities in the dataset to a yield curve subset. e.g. should all Italian govt instruments go to a single curve? Can I further split by floater, linker, ccy, etc.

It is as simple as that.

Your data subset is: maturity, yield. Full data set will be: instrument identifier, instrument characteristics [ccy, cpn type, rating, seniority, etc] , maturity, yield.

Answer 2

This is just an add-on to @rrg's answer. The first thing I recommend that you do is to talk to your manager and get a better grasp of the project scope (which you may have done already). More specifically, are they asking you to build issuer level curves (doesn't sound that way), or sector curves (more likely). How do they plan to define the sectors (by rating? by industry? etc.) This can easily become a very large project, so it's important that you know exactly how far they want you to progress.

Now back to tackling the project. @rrg already mentioned that there are really just two steps. With regard to security selection, the rule of thumb is straightforward: 1) If at all possible, pick or overweigh bonds that are liquid, with good pricing information; 2) Select bonds that are comparable and representative of the market of interest. This is not a science and lots of art is involved. For example, this answer provides some tips (NOT rules) on what bonds can be included in building the US Treasury curve – there are a lot of nuances. For corporates, you should at least make sure that the issuers are of similar credit quality and go from there.

You then proceed to fit the curve. For corporates, parametric models (e.g., Nelson-Siegel, Svensson, even single piece "splines") are very popular, particularly if you don't have a lot of bonds that span the entire maturity spectrum. Don't reinvent the wheel. Look at existing codebase (e.g., Quantlib) and go from there.

Finally, some references:

• For building government curves, The U.S. Treasury Yield Curve: 1961 to the Present and Exponentials, Polynomials, and Fourier Series: More Yield Curve Modeling at the Bank of Canada are good starting points.
• For corporates, take a look at Citigroup Pension Liability Index - Revised Methodology and Creating Corporate Bond Spot Yield Curve for Pension Discounting, both of which discuss building high grade corporate curve suitable for pension discounting; both them address bond selection and then go into various levels of details in terms of actual modeling. I'll also link to The Salomon Brothers Pension Discount Curve if you enjoy reading classics.