CDS Options (Payers and Receivers)

The cost of hedging the credit risk of a loan or bond depends on the CDS spread in the future. You use a CDS option to fix that cost now, or to buy or sell the movement of the spread itself.

The right to enter a CDS in the future

A CDS option is an option to enter into a credit default swap (CDS) on a future date (the expiry). The buyer pays the option premium to the seller and, at expiry, chooses whether to enter into the CDS at the spread agreed in advance (the strike spread). How a CDS works is covered in Credit Default Swaps (CDS).

There are two directions. The right to become the protection buyer is a payer option, and the right to become the protection seller is a receiver option. A payer option is the right to pay a fixed rate (the CDS premium), and a receiver option is the right to receive it¹. The buyer does not have to exercise the right and loses only the option premium paid. The option premium is paid once when the trade is agreed, with no other payments during the life of the option¹.

The underlying is a CDS on a single reference entity (single-name) or a CDS index bundling several reference entities². As of November 2021, CDS options mainly reference indices³. Index options are European options, exercisable only at expiry¹. A CDS option is the credit counterpart of an interest rate swaption and is also called a credit swaption. Interest rate swaptions are covered in Swaptions.

An example on Company U's CDS

Consider a hypothetical example in which Bank T buys a payer option on Company U's 5-year CDS, with a notional amount of 10 billion yen, an expiry of 3 months, and a strike spread of 150bp, for an option premium of 50 million yen. Bank T has lent 10 billion yen to Company U and uses the option to hedge the part of the loan's credit risk that comes from valuation losses when the spread widens. The option is knock-out: it ceases to exist if a credit event occurs at Company U before expiry.

If the market spread on Company U's 5-year CDS at expiry is above 150bp, Bank T can exercise and enter into a CDS to buy protection at 150bp. Because it buys at a lower rate than the market, the difference is the amount gained by exercising. With the present value of 1bp of spread set at 4 million yen, each 1bp of difference is worth 4 million yen⁴. If the market spread is 150bp or below, Bank T does not exercise and loses 50 million yen.

Profit and loss include the option premium. The break-even point is 150bp + 50 million yen ÷ 4 million yen = 162.5bp.

Figure description

The profit or loss at expiry of Bank T, which bought a payer option with a strike spread of 150bp. The horizontal axis is the CDS spread at expiry, and the vertical axis shows profit or loss as a spread width in bp. Because the axis is in bp, the premium of 50 million yen corresponds to 12.5bp. At 150bp or below the loss is constant at 12.5bp (the premium), and above 150bp the profit rises with a slope of 1.

A receiver option works in the opposite direction. With a strike spread of 150bp, the lower the spread at expiry falls below 150bp, the more it gains, because the holder can sell protection at a rate higher than the market.

Strike spread and forward spread

The spread at which the value of a CDS starting at expiry is zero is the forward spread⁵. The value of the option depends on the difference between the strike spread and the forward spread. For indices, only the spread of trades starting now is quoted in the market, and the spread of trades starting at expiry is calculated from it⁶.

The terms in the money, at the money, and out of the money are defined as follows for indices quoted in spread¹.

For options on indices quoted in price (such as CDX.NA.HY), the strike price is compared with the index price, and the directions reverse. A payer option is in the money when the strike price is above the index price¹. The strike spread of a CDX.NA.IG option is in bp, and the strike price of a CDX.NA.HY option is in percent⁷.

With the spread as the underlying, the payer's profit or loss has the shape of a call option, as in the figure above. The IHS Markit document, however, describes a payer option as comparable to a put option and a receiver option to a call option, the reverse of the names used when the spread is the underlying¹.

Knock-out and loss compensation

An option that ceases to exist if a credit event occurs at the reference entity before expiry is a knock-out option. Payer options can be knock-out or non-knock-out².

For options on a single reference entity, the paper by Morini and Brigo treats them as knock-out options whose value is zero after default⁸. In the example, Bank T's payer option would pay nothing if a credit event occurred at Company U before expiry, while the loan would suffer a loss.

An index option does not change when a constituent suffers a credit event and keeps referencing the version of the index it was bought on⁹. A buyer who exercises a payer option receives compensation for the losses from credit events up to expiry. This compensation is called front-end protection⁶. A buyer who exercises a receiver option pays that amount⁹. Because the compensation is received only on exercise, it enters the decision to exercise¹⁰.

Deep diveStrike adjustment on a CDX.NA.HY receiver option

The IHS Markit document gives an example from October 2019: a receiver option on CDX.NA.HY 5-year (Series 33) with a notional amount of USD 100 million, an expiry of 3 months, and a strike of 107% (clean price), bought for a premium of 30.65bp (USD 306,500). Before expiry, one constituent (weight 1%) suffered a credit event, and the recovery rate was set at 9.25%⁹.

The adjusted strike is found with the following formula.

$$1 - \frac{(1 - K) \times IF_{\text{old}} - (1 - R) \times w}{IF_{\text{new}}}$$

$K$ is the original strike (1.07), $IF_{\text{old}}$ and $IF_{\text{new}}$ are the index factors before and after the credit event (1 and 0.99), $R$ is the recovery rate (0.0925), and $w$ is the weight of the name (0.01). In this example the result is 107.9874%. The index price at expiry, 109.4164, is above it, so the buyer gains by exercising¹¹.

The Black model formula and open issues

The basic framework for the price is the Black model, with the forward spread assumed to follow a lognormal distribution. The values of the payer and receiver are given by the following formulas¹².

$$V_{\text{payer}} = A \left[ S \, N(d_1) - K \, N(d_2) \right]$$ $$V_{\text{receiver}} = A \left[ K \, N(-d_2) - S \, N(-d_1) \right]$$ $$d_1 = \frac{\ln(S/K) + \tfrac{1}{2} \sigma^2 T}{\sigma \sqrt{T}}, \quad d_2 = d_1 - \sigma \sqrt{T}$$

Here, $S$ is the forward spread, $K$ is the strike spread, and $\sigma$ is the volatility of the forward spread. The expiry is $T$ years away, and $N$ is the standard normal cumulative distribution function. The factor $A$ is the present value of one unit of spread on the CDS starting at expiry, which takes the default of the reference entity into account. Multiplying by the notional amount gives the amount of money.

For index options, adding the value of front-end protection to the price does not capture the fact that the compensation affects the decision to exercise. Pedersen pointed out this flaw in 2003. In practice it is corrected by using, as $S$, a loss-adjusted spread: the protection leg value plus the front-end protection value, divided by $A$⁵.

Morini and Brigo argue in a 2007 paper that problems remain with that method¹³.

• The definition of the spread does not hold in general.
• The price is undefined in some cases.
• The numeraire (the quantity used as the unit for measuring prices) is not strictly positive.

The paper states that a difference negligible for standard options in normal markets becomes large for non-standard options or in stressed markets¹⁴.

The Greeks (such as delta, gamma, vega, and theta) are also used to measure risk, as for options on other assets¹.

What CDS options are used for

One use is fixing the cost of hedging against a widening spread on a loan. A payer buyer can fix, at today's trade, the upper limit of the rate at which protection will be bought in the future⁶. Take the example with the current spread of Company U at 150bp and the loan's valuation sensitivity set equal to the CDS's, at 4 million yen per 1bp. If the spread at expiry widens to 200bp, the valuation loss on the loan is about 200 million yen, but the option pays 200 million yen, so the net result is only the 50 million yen premium as a loss. If it narrows to 100bp, the valuation gain on the loan is about 200 million yen and the option loses 50 million yen, for a net gain of about 150 million yen.

At 150bp or below the premium is not returned, so the option reduces the loss when the spread widens and, when it narrows, takes the premium out of the gain.

Another use is trading spread movements and volatility. CDS options are also used for directional trades, yield enhancement through option carry, and trades comparing implied and realized volatility³. The seller receives 50 million yen, but in the example the loss grows as the spread at expiry widens beyond 162.5bp, reaching 150 million yen at 200bp.

Risks and trading practice

The buyer's loss is limited to the premium, but the seller's loss grows as the spread widens. The holder of a knock-out option bears the risk that the hedge disappears at a credit event before expiry.

As of November 2021, index options have expiries from 1 month to about 12 months and mainly reference the latest series at 5 years. Expiry is on the third Wednesday of each month, and trading is over the counter and cleared¹. Under the product terms for CDX.NA.IG that tpSEF Inc. filed with the CFTC in October 2014, the swaption is physically settled and exercisable only at expiry, and exercise starts a CDS on the index¹⁵.

Notes

1. IHS Markit, "CDS Indices Primer" (external site) (November 2021), page 30, "Overview" and "CDS Index Option mechanics". ↩ ↩² ↩³ ↩⁴ ↩⁵ ↩⁶ ↩⁷ ↩⁸

2. The same document (external site), page 37, "Credit Swaptions – aka Credit Options". ↩ ↩²

3. The same document (external site), page 13, "Use cases", "Options/Volatility Trading". ↩ ↩²

4. Morini and Brigo (external site), equations 6 and 9 on page 7, give the payer value as the present value per basis point times the spread difference. The example holds this value constant regardless of the spread at expiry. ↩

5. Morini and Brigo, "Arbitrage-free Pricing of Credit Index Options" (external site) (version of December 2007), page 7, "The Credit Index Option". ↩ ↩²

6. The same paper (external site), page 6, "The Forward Credit Index" and "The Credit Index Option". ↩ ↩² ↩³

7. IHS Markit, "CDS Indices Primer" (external site), page 35, "Appendix 4: Swaptions", Option Premium Units for CDX.NA.IG, CDX.NA.HY, iTraxx Europe, and iTraxx Crossover. ↩ ↩²

8. Morini and Brigo (external site), page 10, end of "Subfiltrations for single issuer". ↩

9. IHS Markit, "CDS Indices Primer" (external site), page 31, "Credit events" and "CDS Index Option trade example". ↩ ↩² ↩³ ↩⁴

10. Morini and Brigo (external site), page 3, "Introduction". ↩

11. IHS Markit, "CDS Indices Primer" (external site), page 32, "On option expiry date". ↩

12. Morini and Brigo (external site), pages 7–8, equation 10 and the receiver price formula. The paper's Black function notation is split here into expiry T and volatility σ. ↩

13. Morini and Brigo (external site), page 8, section 3.1, "Problems of the market formulas". ↩

14. Morini and Brigo (external site), page 24, "Conclusion". ↩

15. tpSEF Inc., "Terms and Conditions (CDX.NA.IG)" (external site) (Exhibit B of the filing dated October 30, 2014), "Swaptions on the Above". ↩