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cdsprice

Determine price for credit default swap

Syntax

[Price,AccPrem,PaymentDates,PaymentTimes,PaymentCF]
= cdsprice(ZeroData,ProbData,Settle,Maturity,ContractSpread)

[Price,AccPrem,PaymentDates,PaymentTimes,PaymentCF]
= cdsprice(___,Name,Value)

Description

example

[Price,AccPrem,PaymentDates,PaymentTimes,PaymentCF] = cdsprice(ZeroData,ProbData,Settle,Maturity,ContractSpread) computes the price, or the mark-to-market value for CDS instruments.

Note

Alternatively, you can use the Financial Instruments Toolbox™ CDS (Financial Instruments Toolbox) object to price credit default swaps. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments (Financial Instruments Toolbox).

example

[Price,AccPrem,PaymentDates,PaymentTimes,PaymentCF] = cdsprice(___,Name,Value) adds optional name-value pair arguments.

Examples

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Determine the Price for a Credit Default Swap

Open Live Script

This example shows how to use cdsprice to compute the clean price for a CDS contract using 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);
ContractSpread = 135;

[Price,AccPrem] = cdsprice(ZeroData,ProbData,Settle,Maturity,ContractSpread)

Price = 1.5461e+04

AccPrem = 10500

Input Arguments

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`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 cdsprice 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 the 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, cdsprice 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, cdsprice also accepts serial date numbers as inputs, but they are not recommended.

Data Types: char | string | datetime

`ContractSpread` — Contract spreads
numeric

Contract spreads, specified as a N-by-1 vector of spreads, expressed in basis points.

Data Types: double

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: [Price,AccPrem] = cdsprice(ZeroData,ProbData,Settle,Maturity,ContractSpread,'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

`Notional` — Contract notional values
`10MM` (default) | positive or negative integer

Contract notional values, specified as the comma-separated pair consisting of 'Notional' and a N-by-1vector of integers. Use positive integer values for long positions and negative integer values for short positions.

Data Types: double

`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 'ZeroCmpounding' 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 an integer with values that are identical to Basis.

Data Types: double

Output Arguments

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`Price` — CDS clean prices
vector

CDS clean prices, returned as a N-by-1 vector.

`AccPrem` — Accrued premiums
vector

Accrued premiums, 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.

`PaymentCF` — Payments
matrix

Payments, returned as a N-by-numCF matrix.

More About

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CDS Price

The price or mark-to-market (MtM) value of an existing CDS contract.

The CDS price is computed using the following formula:

CDS price = Notional * (Current Spread - Contract Spread) * RPV01

Current Spread is the current breakeven spread for a similar contract, according to current market conditions. RPV01 is the 'risky present value of a basis point,' the present value of the premium payments, considering the default probability. This formula assumes a long position, and the right side is multiplied by -1 for short positions.

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:

$R P V 01 = \sum_{j = 1}^{N} Z (t j) Δ (t j - 1, t j, B) Q (t j)$

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

$R P V 01 \approx \frac{1}{2} \sum_{j = 1}^{N} Z (t j) Δ (t j - 1, t j, B) (Q (t j - 1) + Q (t j))$

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:

$P r o t e c t i o n L e g = \int_{0}^{T} Z (τ) (1 - R) d P D (τ)$

$\approx (1 - R) \sum_{i = 1}^{M} Z (τ i) (P D (τ i) - P D (τ i - 1))$

$= (1 - R) \sum_{i = 1}^{M} Z (τ i) (Q (τ i - 1) - Q (τ i))$

where the integral is approximated with a finite sum over the discretization τ₀ = 0,τ₁,...,τ_M = T.

If the spread of an existing CDS contract is S_C, and the current breakeven spread for a comparable contract is S₀, the current price, or mark-to-market value of the contract is given by:

MtM = Notional (S₀ –S_C)RPV01

This assumes a long position from the protection standpoint (protection was bought). For short positions, the sign is reversed.

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

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R2022b: Serial date numbers not recommended

Although cdsprice 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.

cdsprice

Syntax

Description

Examples

Determine the Price for a Credit Default Swap

Input Arguments

`ZeroData` — Zero rate data
vector | `IRDataCurve` object

`ProbData` — Default probability values
matrix

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

`Maturity` — Maturity date
datetime array | string array | date character vector

`ContractSpread` — Contract spreads
numeric

Name-Value Arguments

`RecoveryRate` — Recovery rate
`0.4` (default) | decimal

`Period` — Premium payment frequency
`4` (default) | numeric with values `1`, `2`, `3`, `4`, `6` or `12`

`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

`PayAccruedPremium` — Flag for accrued premiums paid upon default
`true` (default) | integer with value `1` or `0`

`Notional` — Contract notional values
`10MM` (default) | positive or negative integer

`TimeStep` — Number of days as time step for numerical integration
`10` (days) (default) | nonnegative integer

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

`ZeroBasis` — Basis of the zero curve
`0` (actual/actual) (default) | integer with value of `0` to `13`

Output Arguments

`Price` — CDS clean prices
vector

`AccPrem` — Accrued premiums
vector

`PaymentDates` — Payment dates
matrix

`PaymentTimes` — Payment times
matrix

`PaymentCF` — Payments
matrix

More About

CDS Price

Algorithms

References

Version History

R2022b: Serial date numbers not recommended

See Also

Topics

cdsprice

Syntax

Description

Examples

Determine the Price for a Credit Default Swap

Input Arguments

ZeroData — Zero rate data vector | IRDataCurve object

ProbData — Default probability values matrix

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

Maturity — Maturity date datetime array | string array | date character vector

ContractSpread — Contract spreads numeric

Name-Value Arguments

RecoveryRate — Recovery rate 0.4 (default) | decimal

Period — Premium payment frequency 4 (default) | numeric with values 1, 2, 3, 4, 6 or 12

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

PayAccruedPremium — Flag for accrued premiums paid upon default true (default) | integer with value 1 or 0

Notional — Contract notional values 10MM (default) | positive or negative integer

TimeStep — Number of days as time step for numerical integration 10 (days) (default) | nonnegative integer

ZeroCompounding — Compounding frequency of the zero curve 2 (semiannual) (default) | integer with value of 1,2,3,4,6,12, or –1

ZeroBasis — Basis of the zero curve 0 (actual/actual) (default) | integer with value of 0 to 13

Output Arguments

Price — CDS clean prices vector

AccPrem — Accrued premiums vector

PaymentDates — Payment dates matrix

PaymentTimes — Payment times matrix

PaymentCF — Payments matrix

More About

CDS Price

Algorithms

References

Version History

R2022b: Serial date numbers not recommended

See Also

Topics

`ZeroData` — Zero rate data
vector | `IRDataCurve` object

`ProbData` — Default probability values
matrix

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

`Maturity` — Maturity date
datetime array | string array | date character vector

`ContractSpread` — Contract spreads
numeric

`RecoveryRate` — Recovery rate
`0.4` (default) | decimal

`Period` — Premium payment frequency
`4` (default) | numeric with values `1`, `2`, `3`, `4`, `6` or `12`

`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

`PayAccruedPremium` — Flag for accrued premiums paid upon default
`true` (default) | integer with value `1` or `0`

`Notional` — Contract notional values
`10MM` (default) | positive or negative integer

`TimeStep` — Number of days as time step for numerical integration
`10` (days) (default) | nonnegative integer

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

`ZeroBasis` — Basis of the zero curve
`0` (actual/actual) (default) | integer with value of `0` to `13`

`Price` — CDS clean prices
vector

`AccPrem` — Accrued premiums
vector

`PaymentDates` — Payment dates
matrix

`PaymentTimes` — Payment times
matrix

`PaymentCF` — Payments
matrix