cdsspread

Determine spread of credit default swap

Syntax

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

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

Description

[Spread,PaymentDates,PaymentTimes,] = cdsspread(ZeroData,ProbData,Settle,Maturity,) computes the spread of the CDS.

[Spread,PaymentDates,PaymentTimes,] = cdsspread(___,Name,Value) adds optional name-value pair arguments.

Examples

Determine the Spread of a Credit Default Swap

This example shows how to use cdsspread to compute the spread (in basis points) for a CDS contract with the following data.

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);

Spread = cdsspread(ZeroData,ProbData,Settle,Maturity)

Spread = 
148.2705

Input Arguments

ZeroData — Zero rate data

vector | IRDataCurve object

Zero rate data, specified as a M-by-2 vector of dates, using a serial date number format, and zero rates or an IRDataCurve object of zero rates.

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

For more information on an IRDataCurve (Financial Instruments Toolbox) object, see Creating an IRDataCurve Object (Financial Instruments Toolbox).

Data Types: double | object

ProbData — Default probability values

matrix

Default probability values, specified as a P-by-2 matrix with dates, using a serial date number format, and corresponding cumulative default probability values.

Data Types: double

Settle — Settlement date

datetime scalar | string scalar | date character vector

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

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

Data Types: char | string | datetime

Maturity — Maturity date

datetime array | string array | date character vector

Maturity date, specified as a N-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, cdsspread 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: Spread = cdsspread(ZeroData,ProbData,Settle,Maturity,'Basis',7,'BusinessDayConvention','previous')

Note

Any optional input of size N-by-1 is also acceptable as an array of size 1-by-N, or as a single value applicable to all contracts. Single values are internally expanded to an array of size N-by-1.

RecoveryRate — Recovery rate

0.4 (default) | decimal

Recovery rate, specified as the comma-separated pair consisting of 'RecoveryRate' and a N-by-1 vector of recovery rates, specified as a decimal from 0 to 1.

Data Types: double

Period — Premium payment frequency

4 (default) | numeric with values 1, 2, 3, 4, 6 or 12

Premium payment frequency, specified as the comma-separated pair consisting of 'Period' and a N-by-1 vector with values of 1, 2, 3, 4, 6, or 12.

Data Types: double

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

Business day conventions, specified as the comma-separated pair consisting of 'BusinessDayConvention' and a character vector. 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 (for example, 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

PayAccruedPremium — Flag for accrued premiums paid upon default

true (default) | integer with value 1 or 0

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

Data Types: logical

TimeStep — Number of days as time step for numerical integration

10 (days) (default) | nonnegative integer

Number of days to take as time step for the numerical integration, specified as the comma-separated pair consisting of 'TimeStep' and a nonnegative integer.

Data Types: double

ZeroCompounding — Compounding frequency of the zero curve

2 (semiannual) (default) | integer with value of 1,2,3,4,6,12, or –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

Data Types: double

ZeroBasis — Basis of the zero curve

0 (actual/actual) (default) | integer with value of 0 to 13

Basis of the zero curve, specified as the comma-separated pair consisting of 'ZeroBasis' and a positive integer with values that are identical to Basis.

Data Types: double

Output Arguments

Spread — Spreads (in basis points)

vector

Spreads (in basis points), returned as a N-by-1 vector.

PaymentDates — Payment dates

matrix

Payment dates, returned as a N-by-numCF matrix.

PaymentTimes — Payment times

matrix

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

More About

CDS Spread

The market, or breakeven, spread value of a CDS.

The CDS spread can be computed by equating the value of the protection leg with the value of the premium leg:

Market Spread * RPV01 = Value of Protection Leg

The left side corresponds to the value of the premium leg, and this has been decomposed as the product of the market or breakeven spread times the RPV01 or 'risky present value of a basis point' of the contract. The latter is the present value of the premium payments, considering the default probability. The Market Spread can be computed as the ratio of the value of the protection leg, to the RPV01 of the contract. cdsspread returns the resulting spread in basis points.

Algorithms

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, t₀ = 0 is the valuation date, and t₁,...,t_n = T are the premium payment dates over the life of the contract,T is the maturity of the contract, Z(t) is the discount factor for a payment received at time t, and Δ(t_j-1, t_j, B) is a day count between dates t_j-1 and t_j corresponding to a basis B.

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 τ₀ = 0,τ₁,...,τ_M = T.

A breakeven spread S₀ makes the value of the premium and protection legs equal. It follows that:

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

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.

Version History

Introduced in R2010b

R2022b: Serial date numbers not recommended

Although cdsspread 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.