Note: This page has been translated by MathWorks. Please click here

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

Determine spread of credit default swap

```
[Spread,PaymentDates,PaymentTimes,]
= cdsspread(ZeroData,ProbData,Settle,Maturity,)
```

```
[Spread,PaymentDates,PaymentTimes,]
= cdsspread(___,Name,Value)
```

`[`

computes
the spread of the CDS.`Spread`

,`PaymentDates`

,`PaymentTimes`

,]
= cdsspread(`ZeroData`

,`ProbData`

,`Settle`

,`Maturity`

,)

`[`

adds
optional name-value pair arguments.`Spread`

,`PaymentDates`

,`PaymentTimes`

,]
= cdsspread(___,`Name,Value`

)

The premium leg is computed as the product of a spread *S* and
the risky present value of a basis point (`RPV01`

).
The `RPV01`

is given by:

$$RPV01={\displaystyle \sum _{j=1}^{N}Z(tj})\Delta (tj-1,tj,B)Q(tj)$$

when no accrued premiums are paid upon default, and it can be approximated by

$$RPV01\approx \frac{1}{2}{\displaystyle \sum _{j=1}^{N}Z(tj})\Delta (tj-1,tj,B)(Q(tj-1)+Q(tj))$$

when accrued premiums are paid upon default. Here, *t _{0}* =

`0`

is
the valuation date, and The protection leg of a CDS contract is given by the following formula:

$$ProtectionLeg={\displaystyle {\int}_{0}^{T}Z(\tau )(1-R)dPD(}\tau )$$

$$\approx (1-R){\displaystyle \sum _{i=1}^{M}Z(\tau i)(PD}(\tau i)-PD(\tau i-1))$$

$$=(1-R){\displaystyle \sum _{i=1}^{M}Z(\tau i)(Q}(\tau i-1)-Q(\tau i))$$

where the integral is approximated with a finite sum over the
discretization *τ _{0}* =

`0`

,A breakeven spread *S _{0}* makes
the value of the premium and protection legs equal. It follows that:

$$S0=\frac{ProtectionLeg}{RPV01}$$

[1] Beumee, J., D. Brigo, D. Schiemert, and G. Stoyle. *“Charting
a Course Through the CDS Big Bang.” * Fitch Solutions,
Quantitative Research, Global Special Report. April 7, 2009.

[2] Hull, J., and A. White. “Valuing Credit Default Swaps
I: No Counterparty Default Risk.” *Journal of Derivatives.* Vol.
8, pp. 29–40.

[3] O'Kane, D. and S. Turnbull. *“Valuation of
Credit Default Swaps.” * Lehman Brothers, Fixed
Income Quantitative Credit Research, April 2003.

`IRDataCurve`

| `cdsbootstrap`

| `cdsprice`

- Finding Breakeven Spread for New CDS Contract
- Valuing an Existing CDS Contract
- Converting from Running to Upfront
- First-to-Default Swaps (Financial Instruments Toolbox)
- Pricing a CDS Index Option (Financial Instruments Toolbox)
- Credit Default Swap (CDS)

Was this topic helpful?