Derive historical price of a corporate bond using current market quotes

External question — Quantitative Finance Stack Exchange Author: darkuss Original post: https://quant.stackexchange.com/questions/81471 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I have a corporate bond, and current broker dealer quotes, I want to determine the price for that bond say 10 days in the past, what would be the best method? Considering there are no historical trade prices available. Should I take the current spread above the swap rate and just apply it to the 10 days old swap curve and date change, or should I adjust the spread and how, based of what?

External answer — Quantitative Finance Stack Exchange Author: Dimitri Vulis Original post: https://quant.stackexchange.com/a/81472 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Yes, the assumption that Z-spreads don't change over such short time horizon, and using the current swap curve looks good to me. It may be even better to identify the corresponding credit index (i.e. HY or IG, CDX for USD, Itraxx for EUR), (convert it to spread if it is HY quoted as price), and assume that your bond's Z-spread changes by the same amount as the index spread, i.e. "credit beta" 1. If you have some history of traded spreads, for this issuer's various bonds, e.g. from TDH (finra Trace), you can even try to regress the changes in traded Z-spreads against changes in the index spread, to get some historical beta, or to support the simplest assumption that the spread doesn't move. Of the bond is callable, then you should use OAS rather than Z-spread, and use implied vols and any other market data from the same date as your swap curve. If the bond is very high yield, then using Z-spread may overstate bond price's sensitivity to interest rates. It might be better to get some actual assumption for loss given default, back out a CDS spread, and use that instead. But you should have some controls to detect that some major news moved the entire market a lot, or idiosyncratic to this corporate issuer, making these assumptions more doubtful.