cdsoptprice
Price payer and receiver credit default swap options
Syntax
Description
[
computes the price of payer and receiver credit default swap options.Payer
,Receiver
] = cdsoptprice(ZeroData
,ProbData
,Settle
,OptionMaturity
,CDSMaturity
,Strike
,SpreadVol
)
Note
Alternatively, you can use the CDSOption
object to price credit default swap options. For
more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
[
computes the price of payer and receiver credit default swap options with
additional options specified by one or more Payer
,Receiver
] = cdsoptprice(___,Name,Value
)Name,Value
pair
arguments.
Examples
Obtain Payer and Receiver Values for a Credit Default Swap Option
Use cdsoptprice
to generate Payer
and Receiver
values for a credit default swap option.
Settle = datenum('12-Jun-2012'); OptionMaturity = datenum('20-Sep-2012'); CDSMaturity = datenum('20-Sep-2017'); OptionStrike = 200; SpreadVolatility = .4; Zero_Time = [.5 1 2 3 4 5]'; Zero_Rate = [.5 .75 1.5 1.7 1.9 2.2]'/100; Zero_Dates = daysadd(Settle,360*Zero_Time,1); ZeroData = [Zero_Dates Zero_Rate]; Market_Time = [1 2 3 5 7 10]'; Market_Rate = [100 120 145 220 245 270]'; Market_Dates = daysadd(Settle,360*Market_Time,1); MarketData = [Market_Dates Market_Rate]; ProbData = cdsbootstrap(ZeroData, MarketData, Settle); [Payer,Receiver] = cdsoptprice(ZeroData, ProbData, Settle,... OptionMaturity, CDSMaturity, OptionStrike, SpreadVolatility)
Payer = 223.5780
Receiver = 22.7460
Input Arguments
ZeroData
— Zero rates
vector | IRDataCurve
object
Zero rates, specified by using a
M
-by-2
vector of dates and zero
rates or an IRDataCurve
object of zero rates. For more
information on an IRDataCurve
object, see
Creating an IRDataCurve Object..
Data Types: double
| object
ProbData
— Probability of default
array
Probability of default, specified as a
P
-by-2
array of dates and default
probabilities.
Data Types: double
Settle
— Settlement date
scalar for serial nonnegative date number | scalar for date character vector
Settlement date, specified as a scalar using a serial nonnegative date
number or date character vector. Settle
must be earlier
than the OptionMaturity
date.
Data Types: double
| char
OptionMaturity
— Option maturity dates
serial nonnegative date number | date character vector
Option maturity dates, specified as an
NINST
-by-1
vector using a serial
nonnegative date number or date character vector.
Data Types: double
| char
CDSMaturity
— CDS maturity dates
serial nonnegative date number | date character vector
CDS maturity dates, specified as an
NINST
-by-1
vector using a serial
nonnegative date number or date character vector.
Data Types: double
| char
Strike
— Option strikes in basis points
vector
Option strikes in basis points, specified as an
NINST
-by-1
vector.
Data Types: double
SpreadVol
— Annualized credit spread volatilities
positive decimal
Annualized credit spread volatilities, specified an
NINST
-by-1
vector of positive
decimals.
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: [Payer,Receiver] =
cdsoptprice(ZeroData,ProbData,Settle,OptionMaturity,CDSMaturity,OptionStrike,SpreadVolatility)
AdjustedForwardSpread
— Adjusted forward spread in basis points
unadjusted forward spread normally used for
single-name CDS options (default) | vector
Adjusted forward spread in basis points, specified as the
comma-separated pair consisting of
'AdjustedForwardSpread'
and an
NINST
-by-1
vector.
Data Types: double
Basis
— Day count basis
0
(actual/actual) (default) | integer from 0
to 13
Day count basis, specified as the comma-separated pair consisting of
'Basis'
and an
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 a 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
Knockout
— Indicator of knockout
False
(default) | vector
Indicator of knockout, specified as the comma-separated pair
consisting of 'Knockout'
and an
NINST
-by-1
vector of boolean
flags. If the credit default swaptions is a knockout, the flag is
True
, otherwise it is
False
.
Data Types: logical
PayAccruedPremium
— Indicator of accrued premium
True
(default) | vector
Indicator of accrued premium, specified as the comma-separated pair
consisting of 'PayAccruedPremium'
and an
NINST
-by-1
vector of boolean
flags. If accrued premiums are paid upon default, the flag is
True
, otherwise it is
False
.
Data Types: logical
Period
— Premiums per year of CDS
4
per year (default) | vector
Premiums per year of CDS, specified as the comma-separated pair
consisting of 'Period'
and a
NINST
-by-1
vector. Allowed
values are 1
, 2
,
3
, 4
, 6
,
and 12
.
Data Types: double
RecoveryRate
— Recovery rates
0.4
per year (default) | vector
Recovery rates, specified as the comma-separated pair consisting of
'RecoveryRate'
and a
NINST
-by-1
vector of decimal
values from 0
to 1
.
Data Types: double
ZeroBasis
— Basis of zero curve
0
(actual/actual) (default) | integer from 0
to 13
Basis of zero curve, specified as the comma-separated pair consisting
of 'ZeroBasis'
and an
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
ZeroCompounding
— Compounding frequency of zero curve
2
(default) | integer with value of 1
, 2
,
3
, 4
, 6
,
12
, or -1
Compounding frequency of zero curve, specified as the comma-separated
pair consisting of 'ZeroCompounding'
and an integer
with one of the following allowed 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
Output Arguments
Payer
— Payer swap options in Basis
points
vector
Payer swap options in Basis
points, returned as an
NINST
-by-1
vector of
prices.
Receiver
— Receiver swap options in Basis
points
vector
Receiver swap options in Basis
points, returned as an
NINST
-by-1
vector of
prices.
More About
Credit Default Swap Option
A credit default swap (CDS) option, or credit default swaption, is a contract that provides the option holder with the right, but not the obligation, to enter into a credit default swap in the future.
CDS options can either be payer swaptions or receiver swaptions. In a payer swaption, the option holder has the right to enter into a CDS in which they are paying premiums and in a receiver swaption, the option holder is receiving premiums.
Algorithms
The payer and receiver credit default swap options are computed using the Black's model as described in O'Kane [1]:
where
RPV01 is the risky present value of a basis point (see cdsrpv01
).
Φ is the normal cumulative distribution function.
σ is the spread volatility.
t is the valuation date.
tE is the option expiry date.
T is the CDS maturity date.
F is the forward spread (from option expiry to CDS maturity).
K is the strike spread.
FEP is the front-end protection (from option initiation to option expiry).
References
[1] O'Kane, D. Modelling Single-name and Multi-name Credit Derivatives. Wiley, 2008, pp. 156–169.
Version History
Introduced in R2011a
See Also
cdsbootstrap
| cdsspread
| cdsprice
| cdsrpv01
| IRDataCurve
| CDSOption
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