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Trying to understand the idea of a zero-recovery swap, for example, a xccy swap with a default clause that allows you to walk away without any future payment from either side if the counterparty defaults (the reference entity and the counterparty are the same entity).

How is such a trade structured? I understand there is the xccy swap with all associated risks but how does one consider the credit risk element ? Say one day the swap has +MTM in your favor and the next day the counterparty/reference entity defaults, what happens then to the MTM? Does it go to 0? If so, how is this hedged? Thx

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Counterparties A and B have a cross-currency swap that disappears (extinguishes) if credit C has a CDS-like credit event.

The underlying swap could be physical delivery or non-delivery; or many other kinds of swaps, e.g. commodity where the floating leg is again physical delivery or non-delivery commodity prices, versus fixed; vanilla interest rate swaps; accreters; etc. But without loss of generality, we will assume below that there's just one cash flow, i.e. a non-delivery FX forward.

They could be in the form of derivatives or credit-linked notes. In the documentation, it is important to explicitly exclude them from any relevant netting agreements. The language for the C credit event is the same as for a credit default swap or a credit linked note.

These used to be more common before the GFC. Some examples are mentioned in passing in this highly entertainig SEC document https://www.sec.gov/files/litigation/admin/2019/34-87127.pdf , paragraphs 24ff

More commonly, extinguishers are bilateral, meaning that the extinguish irrespective of the mark to market of the underlying swap. A unilateral extinguisher extinguishes if the credit event occurs and the mark to market is above some threshold, e.g. is positive for A, but survives if the mark to market is negative for A.

More commonly, extinguishers are zero-recovery, i.e. just terminate. But I've also seen versions where the recovery was a fraction of the mark to market of the underlying swap, or a fraction of some accreting or amortizing notional.

In a self-referencing extinguisher, the counterparty B and the credit C are the same. But even if they are not, often some "wrong-way" correlation between the counterparties, the reference credit, and the underlyings motivates such trades.

Example: a cross-currency swap, B pays an emerging market local currency to A, and A pays hard currency to B. But also B is either the local sovereign, or a systemically important corporate, so that if B(=C) defaults, then the local currency will substantially devalue, and the hard currency leg that A pays to B would be relatively more valuable. To avoid this scenario, A may be willing to give B better terms, e.g. to pay B more fixed hard currency. When pricing such a trade, as discussed below, the local currency's devaluation on B's default must be taken into account.

Example: a high-yield airline B wants to pay A fixed hard currency and to receive from A floating price of fuel. If the price of fuel goes up, B might be forced into bankruptcy. Without the trade being credit-contingent, A would still owe B lots of money on the floating leg. To avoid this scenario, A might be willing to give B better terms (e.g. receive less fixed hard currency from B).

To price and hedge, you really need liquid CDS on C. You could instead use C's credit-risky bonds instead, but bonds usually aren't liquid enough for this to be practical.

If you have observable C CDS quotes, and some assumptions about the recovery (LGD) on the CDS, then you calculate the risk-neutral survival probabilities (1-PD) for the dates of each cash flow of the swap underlying the extinguisher. The mark to market of a bilateral zero-recovery extinguishing cash flow is very simply the mark to market of a vanilla cash flow discounted by the survival probability. For a cross-currency swap with multiple cash flows, just add up the mark to markets of the cash flows.

E.g. if the vanilla NDF's mark to market is \$10,000, and the risk-neutral probability that C will not default before that date is 80%, then the extinguisher mark to market is \$10,000$\times$80\$=\$8,000. Then A could hedge the extinguisher with an offsetting vanilla NDF on the same currencies, but having only 80% of the notional. If later C looks more/less likely to default, then you dynamically decrease/increase this hedge. More discussion of hedging below.

Of course, this mark to market is Level 3 in the sense of Topic 820 / FASB 157. Since the survival probability calculation depends a lot on the unobservable CDS recovery assumption, you should set aside very conservative reserves for the sensitivity of this calculation to the recovery assumption.

There are two approaches to price unilateral extinguishers. You can run a Monte-Carlo simulation to see how likely the underlying swap's mark to market is to be on the right side of the threshold at the time of C's default. Or, if the unilateral version is more valuable than a bilateral one would be, then you can conservatively ignore the unilateralness, since you cannot monetize it anyway, and price the extinguisher as if it were bilateral.

If C CDS doesn't trade, but there are observable prices for C bonds with maturities comparable to the cash flow dates of the swap, then you can make assumptions about the recovery (LGD) of the bonds, estimate the survival probabilities, and use those to price an extinguisher as above. We will not discuss this approach further.

if C jumps to default immediately, there will be some P&L, and that just cannot be fully hedged, except with an exactly offsetting extinguisher. But it will be partly hedged with C CDS, as discussed in more detail below. But let us consider the observable market factors in the absence of default that drive the mark to market of our running example - extinguishing cross-currency swap.

The first-order deltas:

  • FX spot rate (the FX delta is just the mark to market of the trade)
  • interest rates in both currencies, with term structure, and including the cross-currency basis
  • CDS quotes with term structure

Perturbing any of these market factors will change the mark to market, and hence the sensitivities to the other market factors. Even though the product appears linear, there are material cross-gammas between fx spot, interest rates, and credit (and time). For example, if ceteris paribus the survival probability (from CDS) increases by 1%, then the mark to market, the FX delta, and the IR deltas, all also increase by 1%. If the FX spot moves, then the foreign currency IR delta moves.

There is no FX gamma, but in addition to the cross-gammas, there are some second order sensitivities, then you generally can't completely hedge away:

  • for long enough maturities, there will be some IR gamma
  • the way CDS quotes work, there is some gamma

Is it very useful to have a proper P&L explain that will attribute the P&L to all of the above as well as to the passage of time / carry / rolldown of the IR and CDS curves.

Because the sensitivities change as the market factors change, this product needs dynamic hedging. You hedge the FX delta and the interest rate deltas with vanilla FX forwards, cross-currency swaps, or interest rate swaps, to flatten these deltas to within your tolerance. You hedge the sensitivities to the C CDS quotes with C CDS. (In theory, you could use C's bonds, instead of CDS, but this isn't practical.)

Before you enter the trade, you should run a Monte-Carlo simulation to estimate how much the dynamic hedging might cost, assuming conservative bid-offer spreads on the hedges, and consider this cost in the fees that you will charge.

Note that if C defaults, then the extinguisher will jump to 0, and any CDS hedges will jump to CDS recovery, and these will not offset each other exactly. But also, if prior to C's default, the CDS quotes indicated that the default is imminent, then the mark to market of your extinguisher was already close to 0, and the hedges have mostly been unwound.

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  • $\begingroup$ Thanks very much Dimitri. That's beyond what I expected! You raised a few interesting points on which I need more clarity: 1. The airline example: B getting fuel prices and paying fixed hard currency (EM currency ?), why would A seek to avoid being in a position where they have huge negative MtM against a bankrupt entity ? Wouldn't they just unwind their hedges and pay B MtM ? 2. So structuring such a trade would involve adjusting the terms of a vanilla, 0 MTM swap by changing the terms in B's favour (+MtM for B) and adding credit contingency to zero MtM again ? Thanks vm! $\endgroup$
    – eMe
    Feb 1 at 20:22
  • $\begingroup$ Sure, I'll edit to clarify $\endgroup$ Feb 1 at 21:09

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