Determine price for credit default swap
Determine the Price for a Credit Default Swap
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 = '20-Sep-2010'; ContractSpread = 135; [Price,AccPrem] = cdsprice(ZeroData,ProbData,Settle,Maturity,ContractSpread)
Price = 1.5461e+04
AccPrem = 10500
ZeroData — Zero rate data
Zero rate data, specified as a
of dates and zero rates or an
of zero rates.
ZeroData is an
ZeroData and are redundant inside this
function. In this case, specify these optional parameters when constructing
IRDataCurve object before using the
ProbData — Default probability values
Default probability values, specified as a
with dates and corresponding cumulative default probability values.
Settle — Settlement date
serial date number | date character vector
Settlement date, specified as a scalar serial date number or date character vector. The
Settle date must be earlier than or equal to the
Maturity — Maturity date
serial date number | date character vector
Maturity date, specified as a
of serial date numbers or date character vectors.
ContractSpread — Contract spreads
Contract spreads, specified as a
of spreads, expressed in basis points.
comma-separated pairs of
the argument name and
Value is the corresponding value.
Name must appear inside quotes. You can specify several name and value
pair arguments in any order as
[Price,AccPrem] = cdsprice(ZeroData,ProbData,Settle,Maturity,ContractSpread,'Basis',7,'BusinessDayConvention','previous')
Any optional input of size
also acceptable as an array of size
or as a single value applicable to all contracts. Single values are
internally expanded to an array of size
RecoveryRate — Recovery rate
0.4 (default) | decimal
Recovery rate, specified as the comma-separated pair consisting of
'RecoveryRate' and a
1 vector of recovery
rates, specified as a decimal from
Period — Premium payment frequency
4 (default) | numeric with values
Premium payment frequency, specified as the comma-separated pair consisting of
'Period' and a
1 vector with values of
Basis — Day-count basis of contract
2 (actual/360) (default) | positive integers of the set
[1...13] | vector of positive integers of the set
Day-count basis of the contract, specified as the comma-separated pair consisting of
'Basis' and a positive integer using a
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.
BusinessDayConvention — Business day conventions
(default) | character vector
Business day conventions, specified as the comma-separated pair
'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.
PayAccruedPremium — Flag for accrued premiums paid upon default
true (default) | integer with value
Flag for accrued premiums paid upon default, specified as the comma-separated pair consisting
'PayAccruedPremium' and a
1 vector of Boolean flags
true (default) if accrued premiums are paid
Notional — Contract notional values
10MM (default) | positive or negative integer
Contract notional values, specified as the comma-separated pair consisting of
'Notional' and a
1vector of integers. Use
positive integer values for long positions and negative integer values
for short positions.
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
ZeroCompounding — Compounding frequency of the zero curve
2 (semiannual) (default) | integer with value of
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
ZeroBasis — Basis of the zero curve
0 (actual/actual) (default) | integer with value of
Basis of the zero curve, specified as the comma-separated pair consisting of
'ZeroBasis' and an integer with values that are
Price — CDS clean prices
CDS clean prices, returned as a
AccPrem — Accrued premiums
Accrued premiums, returned as a
PaymentDates — Payment dates
Payment dates, returned as a
PaymentTimes — Payment times
Payment times, returned as a
of accrual fractions.
PaymentCF — Payments
Payments, returned as a
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)
Current Spread is the current breakeven spread
for a similar contract, according to current market conditions.
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
The premium leg is computed as the product of a spread S and
the risky present value of a basis point (
RPV01 is given by:
when no accrued premiums are paid upon default, and it can be approximated by
when accrued premiums are paid upon default. Here, t0 =
the valuation date, and t1,...,tn = 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(tj-1,
tj, B) is a day count between dates tj-1 and tj corresponding
to a basis B.
The protection leg of a CDS contract is given by the following formula:
where the integral is approximated with a finite sum over the
discretization τ0 =
0,τ1,...,τM = T.
If the spread of an existing CDS contract is SC, 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:
Notional (S0 –SC)
This assumes a long position from the protection standpoint (protection was bought). For short positions, the sign is reversed.
 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.
 Hull, J., and A. White. “Valuing Credit Default Swaps I: No Counterparty Default Risk.” Journal of Derivatives. Vol. 8, pp. 29–40.
 O'Kane, D. and S. Turnbull. “Valuation of Credit Default Swaps.” Lehman Brothers, Fixed Income Quantitative Credit Research, April 2003.