cdsrpv01

Compute risky present value of a basis point for credit default swap

Syntax

RPV01 = cdsrpv01(ZeroData,ProbData,Settle,Maturity)

RPV01 = cdsrpv01(___,Name,Value)

[RPV01,PaymentDates,PaymentTimes]
= cdsrpv01(ZeroData,ProbData,Settle,Maturity)

[RPV01,PaymentDates,PaymentTimes]
= cdsrpv01(___,Name,Value)

Description

RPV01 = cdsrpv01(ZeroData,ProbData,Settle,Maturity) computes the risky present value of a basis point (RPV01) for a credit default swap (CDS).

example

RPV01 = cdsrpv01(___,Name,Value) adds optional name-value arguments.

example

[RPV01,PaymentDates,PaymentTimes] = cdsrpv01(ZeroData,ProbData,Settle,Maturity) computes the risky present value of a basis point (RPV01), PaymentDates, and PaymentTimes for a credit default swap (CDS).

example

[RPV01,PaymentDates,PaymentTimes] = cdsrpv01(___,Name,Value) computes the risky present value of a basis point (RPV01), PaymentDates, and PaymentTimes for a credit default swap (CDS) using optional name-value pair arguments.

example

Examples

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Calculate the `RPV01` Value for a CDS

Open Live Script

Calculate the RPV01 value, given the following specification for a CDS.

Settle = '17-Jul-2009'; % valuation date for the CDS
Zero_Time = [.5 1 2 3 4 5]';
Zero_Rate = [1.35 1.43 1.9 2.47 2.936 3.311]'/100;
Zero_Dates = daysadd(Settle,360*Zero_Time,1);
ZeroData = [Zero_Dates Zero_Rate];
ProbData = [daysadd(datenum(Settle),360,1), 0.0247];
Maturity = datetime(2010,9,20);

RPV01 = cdsrpv01(ZeroData,ProbData,Settle,Maturity)

RPV01 = 
1.1651

Input Arguments

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`ZeroData` — Dates and zero rates
object from `IRDataCurve` or vector of dates and zero rates

Dates and zero rates, specified by an M-by-2 vector of dates, using a serial date number format, and zero rates or the IRDataCurve object for zero rates. For more information on an IRDataCurve (Financial Instruments Toolbox) object, see Creating an IRDataCurve Object (Financial Instruments Toolbox).

Data Types: object | double

`ProbData` — Dates and default probabilities
vector of dates and default probabilities

Dates and default probabilities, specified by a P-by-2 array, where dates use a serial date number format.

Data Types: double

`Settle` — Settlement date
datetime scalar | string scalar | date character vector

Settlement date, specified by a scalar datetime, string, or date character vector. This must be earlier than or equal to the dates in Maturity.

To support existing code, cdsrpv01 also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

`Maturity` — CDS maturity date
datetime array | string array | date character vector | serial date number

CDS maturity date, specified by an N-by-1 vector using a datetime array, string array, or date character vectors. The CDS premium payment dates occur at regular intervals, and the last payment occurs on these maturity dates.

To support existing code, cdsrpv01 also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: RPV01 = cdsrpv01(ZeroData,ProbData,Settle,Maturity,'Period',1,'StartDate','20-Sep-2010','Basis',1, 'BusinessDayConvention',actual,'CleanRPV01',true,'PayAccruedPremium',true,'ZeroCompounding',1,'ZeroBasis',1)

`Period` — Number of premium payments per year
`4` (default) | positive integer from the set `[1,2,3,4,6,12]` | vector of positive integers from the set `[1,2,3,4,6,12]`

Number of premium payments per year, specified as the comma-separated pair consisting of 'Period' and an N-by-1 vector. Values are 1, 2, 3, 4, 6, and 12.

Data Types: double

`StartDate` — Dates the CDS premium leg starts
`Settle` date (default) | datetime array | string array | date character vector

Dates when the CDS premium leg actually starts, specified as the comma-separated pair consisting of 'StartDate' and an N-by-1 vector using a datetime array, string array, or date character vectors. Must be on or between the Settle and Maturity dates. For a forward-starting CDS, specify this date as a future date after Settle.

To support existing code, cdsrpv01 also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

`Basis` — Day-count basis of contract
`2` (actual/360) (default) | positive integers of the set `[1...13]` | vector of positive integers of the set `[1...13]`

Day-count basis of the contract, specified as the comma-separated pair consisting of 'Basis' and a positive integer using a NINST-by-1 vector.

0 = actual/actual
1 = 30/360 (SIA)
2 = actual/360
3 = actual/365
4 = 30/360 (PSA)
5 = 30/360 (ISDA)
6 = 30/360 (European)
7 = actual/365 (Japanese)
8 = actual/actual (ICMA)
9 = actual/360 (ICMA)
10 = actual/365 (ICMA)
11 = 30/360E (ICMA)
12 = actual/365 (ISDA)
13 = BUS/252

For more information, see Basis.

Data Types: double

`BusinessDayConvention` — Business day conventions
`actual` (default) | character vector | cell array of character vectors

Business day conventions, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a character vector or N-by-1 cell array of character vectors of business day conventions. The selection for business day convention determines how non-business days are treated. Non-business days are defined as weekends plus any other date that businesses are not open (e.g. statutory holidays). Values are:

actual — Non-business days are effectively ignored. Cash flows that fall on non-business days are assumed to be distributed on the actual date.
follow — Cash flows that fall on a non-business day are assumed to be distributed on the following business day.
modifiedfollow — Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.
previous — Cash flows that fall on a non-business day are assumed to be distributed on the previous business day.
modifiedprevious — Cash flows that fall on a non-business day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

Data Types: char | cell

`CleanRPV01` — Flag for premium accrual
`true` (default) | boolean flag with value `true` or `false`

Flag for premium accrual, specified as the comma-separated pair consisting of 'CleanRPV01' and a N-by-1 vector of Boolean flags, which is true if the premium accrued at StartDate is excluded in the RPV01, and false otherwise.

Data Types: logical

`PayAccruedPremium` — Flag for accrued premium payment
`true` (default) | boolean flag with value `true` or `false`

Flag for accrued premium payment, specified as the comma-separated pair consisting of 'PayAccruedPremium' and a N-by-1 vector of Boolean flags, true if accrued premiums are paid upon default, false otherwise.

Data Types: logical

`ZeroCompounding` — Compounding frequency of zero curve
`2` semiannual compounding (default) | integer with acceptable value [`1,2,3,4,6,12, –1`]

Compounding frequency of the zero curve, specified as the comma-separated pair consisting of 'ZeroCompounding' and an integer with values:

1 — Annual compounding
2 — Semiannual compounding
3 — Compounding three times per year
4 — Quarterly compounding
6 — Bimonthly compounding
12 — Monthly compounding
−1 — Continuous compounding

Note

When ZeroData is an IRDataCurve object, the arguments ZeroCompounding and ZeroBasis are implicit in ZeroData and are redundant inside this function. In that case, specify these optional arguments when constructing the IRDataCurve object before calling this function.

Data Types: double

`ZeroBasis` — Basis of zero curve
`0` (actual/actual) (default) | positive integers of the set `[1...13]` | vector of positive integers of the set `[1...13]`

Basis of the zero curve, specified as the comma-separated pair consisting of 'ZeroBasis' and a positive integer using a NINST-by-1 vector.

0 = actual/actual
1 = 30/360 (SIA)
2 = actual/360
3 = actual/365
4 = 30/360 (PSA)
5 = 30/360 (ISDA)
6 = 30/360 (European)
7 = actual/365 (Japanese)
8 = actual/actual (ICMA)
9 = actual/360 (ICMA)
10 = actual/365 (ICMA)
11 = 30/360E (ICMA)
12 = actual/365 (ISDA)
13 = BUS/252

For more information, see Basis.

Data Types: double

Output Arguments

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`RPV01` — RPV01 value
scalar | vector

RPV01 value, returned as an N-by-1 vector.

`PaymentDates` — Payment dates
scalar | vector

Payment dates, returned as an N-by-numCF matrix of dates.

`PaymentTimes` — Payment times
scalar | vector

Payment times, returned as an N-by-numCF matrix of accrual fractions.

More About

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RPV01

RPV01, associated with a CDS, is the value of a stream of 1-basis-point premiums according to the payment structure of the CDS contract, and considering the default probability over time.

For more information, see [3] and [4] for details.

References

[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.

[4] O'Kane, D. Modelling Single-name and Multi-name Credit Derivatives. Wiley Finance, 2008.

Version History

Introduced in R2013b

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R2022b: Serial date numbers not recommended

Although cdsrpv01 supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.

cdsrpv01

Syntax

Description

Examples

Calculate the `RPV01` Value for a CDS

Input Arguments

`ZeroData` — Dates and zero rates
object from `IRDataCurve` or vector of dates and zero rates

`ProbData` — Dates and default probabilities
vector of dates and default probabilities

`Settle` — Settlement date
datetime scalar | string scalar | date character vector

`Maturity` — CDS maturity date
datetime array | string array | date character vector | serial date number

Name-Value Arguments

`Period` — Number of premium payments per year
`4` (default) | positive integer from the set `[1,2,3,4,6,12]` | vector of positive integers from the set `[1,2,3,4,6,12]`

`StartDate` — Dates the CDS premium leg starts
`Settle` date (default) | datetime array | string array | date character vector

`Basis` — Day-count basis of contract
`2` (actual/360) (default) | positive integers of the set `[1...13]` | vector of positive integers of the set `[1...13]`

`BusinessDayConvention` — Business day conventions
`actual` (default) | character vector | cell array of character vectors

`CleanRPV01` — Flag for premium accrual
`true` (default) | boolean flag with value `true` or `false`

`PayAccruedPremium` — Flag for accrued premium payment
`true` (default) | boolean flag with value `true` or `false`

`ZeroCompounding` — Compounding frequency of zero curve
`2` semiannual compounding (default) | integer with acceptable value [`1,2,3,4,6,12, –1`]

`ZeroBasis` — Basis of zero curve
`0` (actual/actual) (default) | positive integers of the set `[1...13]` | vector of positive integers of the set `[1...13]`

Output Arguments

`RPV01` — RPV01 value
scalar | vector

`PaymentDates` — Payment dates
scalar | vector

`PaymentTimes` — Payment times
scalar | vector

More About

RPV01

References

Version History

R2022b: Serial date numbers not recommended

See Also

Topics

cdsrpv01

Syntax

Description

Examples

Calculate the RPV01 Value for a CDS

Input Arguments

ZeroData — Dates and zero rates object from IRDataCurve or vector of dates and zero rates

ProbData — Dates and default probabilities vector of dates and default probabilities

Settle — Settlement date datetime scalar | string scalar | date character vector

Maturity — CDS maturity date datetime array | string array | date character vector | serial date number

Name-Value Arguments

Period — Number of premium payments per year 4 (default) | positive integer from the set [1,2,3,4,6,12] | vector of positive integers from the set [1,2,3,4,6,12]

StartDate — Dates the CDS premium leg starts Settle date (default) | datetime array | string array | date character vector

Basis — Day-count basis of contract 2 (actual/360) (default) | positive integers of the set [1...13] | vector of positive integers of the set [1...13]

BusinessDayConvention — Business day conventions actual (default) | character vector | cell array of character vectors

CleanRPV01 — Flag for premium accrual true (default) | boolean flag with value true or false

PayAccruedPremium — Flag for accrued premium payment true (default) | boolean flag with value true or false

ZeroCompounding — Compounding frequency of zero curve 2 semiannual compounding (default) | integer with acceptable value [1,2,3,4,6,12, –1]

ZeroBasis — Basis of zero curve 0 (actual/actual) (default) | positive integers of the set [1...13] | vector of positive integers of the set [1...13]

Output Arguments

RPV01 — RPV01 value scalar | vector

PaymentDates — Payment dates scalar | vector

PaymentTimes — Payment times scalar | vector

More About

RPV01

References

Version History

R2022b: Serial date numbers not recommended

See Also

Topics

Calculate the `RPV01` Value for a CDS

`ZeroData` — Dates and zero rates
object from `IRDataCurve` or vector of dates and zero rates

`ProbData` — Dates and default probabilities
vector of dates and default probabilities

`Settle` — Settlement date
datetime scalar | string scalar | date character vector

`Maturity` — CDS maturity date
datetime array | string array | date character vector | serial date number

`Period` — Number of premium payments per year
`4` (default) | positive integer from the set `[1,2,3,4,6,12]` | vector of positive integers from the set `[1,2,3,4,6,12]`

`StartDate` — Dates the CDS premium leg starts
`Settle` date (default) | datetime array | string array | date character vector

`Basis` — Day-count basis of contract
`2` (actual/360) (default) | positive integers of the set `[1...13]` | vector of positive integers of the set `[1...13]`

`BusinessDayConvention` — Business day conventions
`actual` (default) | character vector | cell array of character vectors

`CleanRPV01` — Flag for premium accrual
`true` (default) | boolean flag with value `true` or `false`

`PayAccruedPremium` — Flag for accrued premium payment
`true` (default) | boolean flag with value `true` or `false`

`ZeroCompounding` — Compounding frequency of zero curve
`2` semiannual compounding (default) | integer with acceptable value [`1,2,3,4,6,12, –1`]

`ZeroBasis` — Basis of zero curve
`0` (actual/actual) (default) | positive integers of the set `[1...13]` | vector of positive integers of the set `[1...13]`

`RPV01` — RPV01 value
scalar | vector

`PaymentDates` — Payment dates
scalar | vector

`PaymentTimes` — Payment times
scalar | vector