Estimating Structured-Bond Recovery from Remaining Cash Flows

# Recovery rate in a structured bond


# Recovery rate in a structured bond












I need to model the recovery rate of a structured bond whose expected cash flows, if the issuer remains solvent, will be very low. For instance, assume that I need to estimate the recovery amount of a bond with an expected cash flow at maturity of 15% of its notional value (i.e.: the expected coupon is -85%).

In order to estimate a recovery in this type of bond:

- Should I still consider the initial bond notional and apply a recovery rate? In such case, with the usual levels of recovery of $\sim$ 0.4 the defaulting scenario would result in a higher payoff than the solvency one, which seems quite odd.

- Which other approaches could be used to estimate the recovery in these types of bonds? (e.g: calculate the recovery based on the non-default market value?)

EDIT: Information added based on comments

## Answer by Brian B (score 2, accepted)

https://quant.stackexchange.com/a/9398

Recovery rates are rarely "modeled" per se, in the sense that most practitioners avoid treating them as random variables. I doubt you want to buck that trend here.

As jeff m implies in the comments, it's the cash flow that you really want to know about, so you'll find it more useful to think in terms of the mechanism behind recovery.

If the issuer defaults, there's going to be a court case, and a whole bunch of lawyers are going to negotiate, under the supervision of a judge, who gets what from the remaining firm assets. Around that time, experts in distressed debt will presumably be trading this bond based on their best guess as to the outcome of those negotiations.

So, what will this bond look like as a claim in those negotiations? Well, normal bonds are often issued such that the coupon more-or-less compensates for default risk and time value of money, so as a shorthand practitioners think of the non-default value of the bond as being equal to the notional, and that's the number that influences recovery cash flow.

Savvy players will know that this bond becomes worth much less over time, so you can expect the notional won't be accepted as a baseline. Instead it will probably be viewed as future cashflows, discounted by a rate somewhere between risk-free and risky.

This is all a roundabout way of saying that I would tend to take a recovery rate $\delta$ as usual, but include a risky discount rate $z$, and then set the recovery value of the instrument, conditional on default at time $\tau$ as the time-dependent value

$$ \sum_{n \ni t_n>\tau} \delta\cdot c_n\cdot \exp\left( -\int_\tau^{t_n} z(s)ds\right) $$

in my pricing formulas.