# CDS Options (Payers and Receivers)

> A CDS option is an option that gives the buyer the right to enter into a CDS at a spread agreed in advance (the strike spread) on a future expiry date. The right to become the protection buyer is a payer option, and the right to become the protection seller is a receiver option. The buyer pays the option premium to the seller when the trade is agreed.

- URL: https://www.derivatives-compass.org/en/credit/cds-options/
- Area: Credit Derivatives › CDS
- Last reviewed: 2026-10-22
- 日本語版: https://www.derivatives-compass.org/ja/credit/cds-options/index.md

## Key points

- Whether the right is exercised depends on the spread at expiry, and the buyer's loss is limited to the premium paid.
- A payer option gains as the spread at expiry rises above the strike spread, and a receiver option gains as it falls below.
- The treatment of credit events before expiry depends on whether the option is knock-out and, for indices, on front-end protection.
- Pricing is based on the Black model, which treats the forward spread as lognormal, and open issues remain in how losses before expiry are treated.
- Uses are fixing a future hedging cost and trading spreads and volatility.

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](https://www.derivatives-compass.org/en/glossary/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](https://www.derivatives-compass.org/en/glossary/credit-default-swap/) (CDS) on a future date (the expiry). The buyer pays the [option premium](https://www.derivatives-compass.org/en/glossary/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)](https://www.derivatives-compass.org/en/credit/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 it[^primer-p30]. The buyer does not have to [exercise](https://www.derivatives-compass.org/en/glossary/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 option[^primer-p30].

The underlying is a CDS on a single reference entity (single-name) or a [CDS index](https://www.derivatives-compass.org/en/glossary/cds-index/) bundling several reference entities[^primer-p37]. As of November 2021, CDS options mainly reference indices[^primer-p13]. Index options are [European options](https://www.derivatives-compass.org/en/glossary/european-option/), exercisable only at expiry[^primer-p30]. 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](https://www.derivatives-compass.org/en/rates/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](https://www.derivatives-compass.org/en/glossary/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](https://www.derivatives-compass.org/en/glossary/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 yen[^rpv01]. If the market spread is 150bp or below, Bank T does not exercise and loses 50 million yen.

| Spread at expiry (bp) | Exercise | Amount gained by exercising (million yen) | Bank T's profit or loss (million yen) | Seller's profit or loss (million yen) |
| --------------------: | -------- | ----------------------------------------: | ------------------------------------: | ------------------------------------: |
|                   100 | No       |                                         0 |                                   −50 |                                   +50 |
|                   150 | No       |                                         0 |                                   −50 |                                   +50 |
|                 162.5 | Yes      |                                        50 |                                     0 |                                     0 |
|                   200 | Yes      |                                       200 |                                  +150 |                                  −150 |
|                   250 | Yes      |                                       400 |                                  +350 |                                  −350 |

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

**Figure 1: Profit or loss of the payer buyer at expiry**

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 spread[^bm-p7]. 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 it[^bm-p6].

The terms [in the money](https://www.derivatives-compass.org/en/glossary/in-the-money/), [at the money](https://www.derivatives-compass.org/en/glossary/at-the-money/), and [out of the money](https://www.derivatives-compass.org/en/glossary/out-of-the-money/) are defined as follows for indices quoted in spread[^primer-p30].

| Right    | In the money                          | At the money | Out of the money |
| -------- | ------------------------------------- | ------------ | ---------------- |
| Payer    | Strike spread below the market spread | Equal        | Above            |
| Receiver | Strike spread above the market spread | Equal        | Below            |

For options on indices quoted in price (such as CDX.NA.HY), the [strike price](https://www.derivatives-compass.org/en/glossary/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 price[^primer-p30]. The strike spread of a CDX.NA.IG option is in bp, and the strike price of a CDX.NA.HY option is in percent[^primer-p35].

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 underlying[^primer-p30].

## 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-out[^primer-p37].

For options on a single reference entity, the paper by Morini and Brigo treats them as knock-out options whose value is zero after default[^bm-p10]. 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 on[^primer-p31]. A buyer who exercises a payer option receives compensation for the losses from credit events up to expiry. This compensation is called front-end protection[^bm-p6]. A buyer who exercises a receiver option pays that amount[^primer-p31]. Because the compensation is received only on exercise, it enters the decision to exercise[^bm-p3].

> **Deep dive: Strike 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%[^primer-p31].
>
> 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 exercising[^primer-p32].

> **For operations and accounting: Handling index versions after exercise**
>
> Because an index option keeps referencing the original version, the version the option references and the new version traded in the market diverge after a credit event. When an option quoted in price is exercised, the strike, a clean price, is adjusted and the amount paid or received includes accrued interest[^primer-p31].

## The Black model formula and open issues

The basic framework for the price is the [Black model](https://www.derivatives-compass.org/en/glossary/black-model/), with the forward spread assumed to follow a lognormal distribution. The values of the payer and receiver are given by the following formulas[^bm-black].

$$
V_{\text{payer}} = A \left[ S \, N(d_1) - K \, N(d_2) \right]
$$

$$
V_{\text{receiver}} = A \left[ K \, N(-d_2) - S \, N(-d_1) \right]
$$

$$
d_1 = \frac{\ln(S/K) + \tfrac{1}{2} \sigma^2 T}{\sigma \sqrt{T}}, \quad d_2 = d_1 - \sigma \sqrt{T}
$$

Here, $$S$$ is the forward spread, $$K$$ is the strike spread, and $$\sigma$$ is the [volatility](https://www.derivatives-compass.org/en/glossary/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 $$A$$[^bm-p7].

Morini and Brigo argue in a 2007 paper that problems remain with that method[^bm-p8].

- The definition of the spread does not hold in general.
- The price is undefined in some cases.
- The [numeraire](https://www.derivatives-compass.org/en/glossary/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 markets[^bm-p24].

The [Greeks](https://www.derivatives-compass.org/en/glossary/greeks/) (such as delta, gamma, vega, and theta) are also used to measure risk, as for options on other assets[^primer-p30].

## 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 future[^bm-p6]. 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 volatility[^primer-p13]. 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.

> **For front office: How premiums are quoted**
>
> Premiums for options on indices such as CDX.NA.IG are quoted in bp of the notional amount[^primer-p35]. At the same scale as the example (a notional amount of 10 billion yen), 50 million yen corresponds to 50bp.

## 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 cleared[^primer-p30]. Under the product terms for CDX.NA.IG that tpSEF Inc. filed with the [CFTC](https://www.derivatives-compass.org/en/glossary/cftc/) in October 2014, the swaption is physically settled and exercisable only at expiry, and exercise starts a CDS on the index[^tpsef-b].

> **For systems professionals: Trade data items**
>
> A design that holds option trades carries the direction of the right (payer or receiver) and the underlying (a reference entity, or an index series and version). It also carries the expiry, the strike spread or strike price, whether the option is knock-out, the quotation method (spread or price), and the option premium. After a credit event, it must be able to calculate the adjusted strike while keeping the reference to the original version.

[^primer-p30]: [IHS Markit, "CDS Indices Primer"](https://cdn.ihsmarkit.com/www/pdf/1221/CDS-Indices-Primer---2021.pdf) (November 2021), page 30, "Overview" and "CDS Index Option mechanics".

[^primer-p37]: [The same document](https://cdn.ihsmarkit.com/www/pdf/1221/CDS-Indices-Primer---2021.pdf), page 37, "Credit Swaptions – aka Credit Options".

[^primer-p13]: [The same document](https://cdn.ihsmarkit.com/www/pdf/1221/CDS-Indices-Primer---2021.pdf), page 13, "Use cases", "Options/Volatility Trading".

[^rpv01]: [Morini and Brigo](https://arxiv.org/pdf/0812.4156), 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.

[^bm-p7]: [Morini and Brigo, "Arbitrage-free Pricing of Credit Index Options"](https://arxiv.org/pdf/0812.4156) (version of December 2007), page 7, "The Credit Index Option".

[^bm-p6]: [The same paper](https://arxiv.org/pdf/0812.4156), page 6, "The Forward Credit Index" and "The Credit Index Option".

[^primer-p35]: [IHS Markit, "CDS Indices Primer"](https://cdn.ihsmarkit.com/www/pdf/1221/CDS-Indices-Primer---2021.pdf), page 35, "Appendix 4: Swaptions", Option Premium Units for CDX.NA.IG, CDX.NA.HY, iTraxx Europe, and iTraxx Crossover.

[^bm-p10]: [Morini and Brigo](https://arxiv.org/pdf/0812.4156), page 10, end of "Subfiltrations for single issuer".

[^primer-p31]: [IHS Markit, "CDS Indices Primer"](https://cdn.ihsmarkit.com/www/pdf/1221/CDS-Indices-Primer---2021.pdf), page 31, "Credit events" and "CDS Index Option trade example".

[^bm-p3]: [Morini and Brigo](https://arxiv.org/pdf/0812.4156), page 3, "Introduction".

[^primer-p32]: [IHS Markit, "CDS Indices Primer"](https://cdn.ihsmarkit.com/www/pdf/1221/CDS-Indices-Primer---2021.pdf), page 32, "On option expiry date".

[^bm-black]: [Morini and Brigo](https://arxiv.org/pdf/0812.4156), 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.

[^bm-p8]: [Morini and Brigo](https://arxiv.org/pdf/0812.4156), page 8, section 3.1, "Problems of the market formulas".

[^bm-p24]: [Morini and Brigo](https://arxiv.org/pdf/0812.4156), page 24, "Conclusion".

[^tpsef-b]: [tpSEF Inc., "Terms and Conditions (CDX.NA.IG)"](https://www.cftc.gov/filings/ptc/ptc110914tpsefsef028.pdf) (Exhibit B of the filing dated October 30, 2014), "Swaptions on the Above".

## Sources

- [CDS Indices Primer](https://cdn.ihsmarkit.com/www/pdf/1221/CDS-Indices-Primer---2021.pdf) — IHS Markit
- [Arbitrage-free Pricing of Credit Index Options: The no-armageddon pricing measure and the role of correlation after the subprime crisis](https://arxiv.org/pdf/0812.4156) — Massimo Morini、Damiano Brigo（arXiv）
- [Terms and Conditions (CDX.NA.IG), Exhibit B of the submission of October 30, 2014](https://www.cftc.gov/filings/ptc/ptc110914tpsefsef028.pdf) — tpSEF Inc.