Modeling Stock Recovery Values After Default

Summary

The document raises a modeling question about whether a stock that can default but retain some value should be represented by a shifted lognormal process with jumps to default. In this proposal, the shift would represent a recovery value or lower bound, reflecting the possibility that restructuring leaves shareholders with value rather than making the stock worthless. It contrasts this idea with jump-to-default models that allow default but do not explicitly represent a positive recovery floor.

The document offers no model specification, derivation, empirical evidence, or practitioner response. It does not establish whether a deterministic shift is an appropriate way to represent recovery, or how such a model would handle uncertainty in recovery value, changing firm conditions, or the timing of default. It is best read as an open modeling question rather than a recommended method or validated strategy.

Key ideas

• Jump-to-default models can represent the possibility of corporate default.
• A stock may retain value after default if the company is restructured.
• The document proposes a shifted lognormal model whose shift represents a recovery value or minimum stock price.
• The proposal is posed as a question and is not supported by analysis or evidence.

Tags

# Modelling stocks with jump to default and recovery value


# Modelling stocks with jump to default and recovery value












Jump to default models (eg Black-Scholes or SV with jump to default) are quite tractable models to model the possibility of default.

However, if a company defaults it doesn't always mean the stock price goes to zero. The company could be restructured for example.

I was wondering if it makes sense to then model such a stock as a shifted lognormal with jump to default, where the constant or deterministic value in the shifted lognormal represents the stock recovery value / the minimum value the stock price can have.

Any suggestions from practitioners in this field?

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