Risk-Neutral Valuation for CLO Tranche Investors

Summary

The document asks whether a lender and an equity holder in a simplified collateralized loan obligation should value their claims using the same risk-neutral probability measure. The lender receives an agreed payment ahead of the borrower, who keeps the residual bond coupons after servicing the debt. The example highlights that these claims have different exposures to default and recovery.

The answer distinguishes the lender’s valuation inputs, which include the borrower’s own default risk and recovery, from the borrower’s exposure to defaults and recoveries on the bonds held in the portfolio. It therefore rejects the idea that one measure must describe both positions identically. The explanation is brief and does not specify a formal model, derive tranche values, or discuss how to calibrate probabilities and dependence assumptions. Its two-party setup is a simplified illustration rather than a full treatment of CLO waterfall structures or market pricing.

Key ideas

• The lender and residual holder have different sources of credit risk.
• The lender’s valuation must account for the borrower’s default and recovery.
• The residual holder’s valuation depends on the bonds’ default risk and recovery.
• The short example does not provide a full CLO valuation framework or calibration method.

Tags

# Will the risk-neutral measure be different for different CLO tranches?


# Will the risk-neutral measure be different for different CLO tranches?












Consider the following derivative (mimicking a CLO):

- B borrows 90 dollars from lender L.

- B buys some bonds worth 100 dollars using his own 10 dollars and the 90 dollars he borrowed. The bonds pay some coupon C.

- Coupons from the bonds go to B, but he has to pay the lender L some agreed upon amount S, so $B$ gets whatever is left over after $L$ is paid.

What are the values of these positions to $L$ and $B$? We know that this is the expected discounted value of the cashflows under the risk-neutral measure $Q$. This measure could for example depend on parameters like the default rate of each bond, and the default correlations amongst all bonds. So $Q$ could be as simple or as fancy as we'd like but my question is, do $L$ and $B$ choose the same measure $Q$?

## Answer by D Stanley (score 1)

https://quant.stackexchange.com/a/84116

No - L's risk neutral measure would take the risk of B defaulting (and the expected recovery) into account, while B's risk neutral measure would be based on the default risk and recovery rate of the bond they bought.

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