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).

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

[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).

[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.

Examples

Calculate the RPV01 Value for a CDS

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

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

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

Credit Default Swap

A Credit Default Swap (CDS) is a financial derivative contract that allows an investor to "swap" or transfer the credit risk of a borrower (usually a corporation or government) to another party.

The parties involved are:

• Protection Buyer — The party that purchases the CDS to protect against the risk of default. They pay periodic premiums (known as the CDS spread) to the protection seller.

• Protection Seller — The party that provides the credit protection and receives the premiums from the protection buyer. In the event of a default, the protection seller is obligated to compensate the protection buyer.

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

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.