# cdsoptprice

Price payer and receiver credit default swap options

## Syntax

## Description

`[`

computes the price of payer and receiver credit default swap options.`Payer`

,`Receiver`

] = cdsoptprice(`ZeroData`

,`ProbData`

,`Settle`

,`OptionMaturity`

,`CDSMaturity`

,`Strike`

,`SpreadVol`

)

`[`

computes the price of payer and receiver credit default swap options with
additional options specified by one or more `Payer`

,`Receiver`

] = cdsoptprice(___,`Name,Value`

)`Name,Value`

pair
arguments.

## Examples

## Input Arguments

## Output Arguments

## More About

## Algorithms

The payer and receiver credit default swap options are computed using the Black's model as described in O'Kane [1]:

$${V}_{Pay(Knockout)}=RPV01(t,{t}_{E},T)(F\Phi ({d}_{1})-K\Phi ({d}_{2}))$$

$${V}_{Rec(Knockout)}=RPV01(t,{t}_{E},T)(K\Phi (-{d}_{2})-F\Phi (-{d}_{1}))$$

$${d}_{1}=\frac{\mathrm{ln}\left(\frac{F}{K}\right)+\frac{1}{2}{\sigma}^{2}({t}_{E}-t)}{\sigma \sqrt{{t}_{E}-t}}$$

$${d}_{2}={d}_{1}-\sigma \sqrt{{t}_{E}-t}$$

$${V}_{Pay(Non-Knockout)}={V}_{Pay(Knockout)}+FEP$$

$${V}_{Pay(Non-Knockout)}={V}_{Rec(Knockout)}$$

where

*RPV01* is the risky present value of a basis point (see `cdsrpv01`

).

*Φ* is the normal cumulative distribution function.

*σ* is the spread volatility.

*t* is the valuation date.

*t _{E}* is the option expiry date.

*T* is the CDS maturity date.

*F* is the forward spread (from option expiry to CDS
maturity).

*K* is the strike spread.

*FEP* is the front-end protection (from option initiation to option
expiry).

## References

[1] O'Kane, D.
*Modelling Single-name and Multi-name Credit Derivatives.*
Wiley, 2008, pp. 156–169.

## Version History

**Introduced in R2011a**