Estimating a Convertible Bond’s Implied Credit Spread with Negative Yield

Summary

The document addresses how to interpret a convertible bond whose yield is negative and how to estimate its implied credit spread. The response attributes the negative yield primarily to the embedded conversion option, which has both conversion value and time value. The proposed approach is to value that option using a Black–Scholes model, subtract the option value from the convertible’s market value to isolate the bond component, and then use a rate calculation to infer its implied credit spread.

This is a brief conceptual answer rather than a worked valuation. It does not provide bond terms, option-model inputs, a specific definition of the rate calculation, or a numerical example. The implied spread therefore depends on the assumptions and accuracy of the option valuation and the remaining bond valuation. The discussion does not establish that spreads can never be negative; it only describes a way to derive an implied spread for the bond portion after accounting for the conversion option.

Key ideas

• A convertible bond’s option value can contribute to a negative quoted yield.
• The conversion option includes both intrinsic conversion value and time value.
• Subtracting an estimated option value can help isolate the bond component for spread analysis.
• The implied credit spread depends on the option valuation and the bond-rate calculation assumptions.

Tags

# Implied credit spread convertible bonds with negative yield


# Implied credit spread convertible bonds with negative yield












I’m trying to understand what happens to the credit spread of a convertible bond when yields of the convertible are negative. I’ve heard there is an implied credit spread as spreads can’t really be negative. I’ve tried looking in the usual sources but I can’t find much specifically related to negative yields. Happy to look at link etc.

## Answer by Brian (score 1)

https://quant.stackexchange.com/a/40707

Negative yields will typically be negative do to the value of option (conversion value + time value). If you subtract out the value of that option as determined by a blackscholes model the remaining value will be the bond component. Using a RATE function will then give you the implied credit spread.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.