The credit spread curve. I: Fundamental concepts, fitting, par-adjusted spread, and expected return
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arXiv
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| Format: | Preprint |
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2022
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| _version_ | 1866929304218107904 |
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| author | Martin, Richard J. |
| author_facet | Martin, Richard J. |
| contents | The notion of a credit spread curve is fundamental in fixed income investing, but in practice it is not `given' and needs to be constructed from bond prices either for a particular issuer, or for a sector rating-by-rating. Rather than attempting to fit spreads -- and as we discuss here, the Z-spread is unsuitable -- we fit parametrised survival curves. By deriving a valuation formula for a risky bond, we explain and avoid the problem that bonds with a high dollar price trade at a higher yield or spread than those with low dollar price (at the same maturity point), even though they do not necessarily offer better value. In fact, a concise treatment of this effect is elusive, and much of the academic literature on risky bond pricing, including a well-known paper by Duffie and Singleton (1997), is fundamentally incorrect. We then proceed to show how to calculate carry, rolldown and relative value for bonds/CDS. Also, once curve construction has been programmed and automated we can run it historically and assess the way a curve has moved over time. This provides the necessary grounding for econometric and arbitrage-free models of curve dynamics, which will be pursued in later work, as well as assessing how the perceived relative value of a particular instrument varies over time. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2201_01330 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | The credit spread curve. I: Fundamental concepts, fitting, par-adjusted spread, and expected return Martin, Richard J. Pricing of Securities Risk Management Statistical Finance The notion of a credit spread curve is fundamental in fixed income investing, but in practice it is not `given' and needs to be constructed from bond prices either for a particular issuer, or for a sector rating-by-rating. Rather than attempting to fit spreads -- and as we discuss here, the Z-spread is unsuitable -- we fit parametrised survival curves. By deriving a valuation formula for a risky bond, we explain and avoid the problem that bonds with a high dollar price trade at a higher yield or spread than those with low dollar price (at the same maturity point), even though they do not necessarily offer better value. In fact, a concise treatment of this effect is elusive, and much of the academic literature on risky bond pricing, including a well-known paper by Duffie and Singleton (1997), is fundamentally incorrect. We then proceed to show how to calculate carry, rolldown and relative value for bonds/CDS. Also, once curve construction has been programmed and automated we can run it historically and assess the way a curve has moved over time. This provides the necessary grounding for econometric and arbitrage-free models of curve dynamics, which will be pursued in later work, as well as assessing how the perceived relative value of a particular instrument varies over time. |
| title | The credit spread curve. I: Fundamental concepts, fitting, par-adjusted spread, and expected return |
| topic | Pricing of Securities Risk Management Statistical Finance |
| url | https://arxiv.org/abs/2201.01330 |