I have a corporate bond curve which stops at 15 year maturity. I want to extrapolate the curve to 25 year maturity.
I'm looking for a reasonable approach, not necessarily deeply technical.
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Corporate bonds are usually priced as some yield above treasuries. You can use this to extrapolate the later tenors. Start by computing the credit spread for the earlier tenors. This is computed by subtracting the corporate curve by the sovereign. Extrapolate the credit spread using spline/linear model assuming it varies across the tenors, if it doesn’t vary you don’t need a model. Simply take the extrapolated values for the credit spread and add it to the sovereign curve. This will give you an estimate of what the yields for the later maturities are.
Use other corporate bond curves for the company in the same sector. If not, use curves with the same rating profile and make adjustments. For example, if you're pricing a Ford bond from 15 to 25 years, you can use GM's credit curve. Let's assume GM's 15 to 25 credit spread curve is 100bp. Then you can use that as a proxy for Ford's 15 to 25 curve and make the necessary changes. There's a lot of hand waiving when pricing these curves but it needs to be reasonable.