cdsoptprice

Price payer and receiver credit default swap options

Syntax

[Payer,Receiver] = cdsoptprice(ZeroData,ProbData,Settle,OptionMaturity,CDSMaturity,Strike,SpreadVol)
[Payer,Receiver] = cdsoptprice(ZeroData,ProbData,Settle,OptionMaturity,CDSMaturity,Strike,SpreadVol,Name,Value)


Description

[Payer,Receiver] = cdsoptprice(ZeroData,ProbData,Settle,OptionMaturity,CDSMaturity,Strike,SpreadVol) computes the price of payer and receiver credit default swap options.

[Payer,Receiver] = cdsoptprice(ZeroData,ProbData,Settle,OptionMaturity,CDSMaturity,Strike,SpreadVol,Name,Value) computes the price of payer and receiver credit default swap options with additional options specified by one or more Name,Value pair arguments.

Input Arguments

ZeroData

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.

ProbData	P-by-2 array of dates and default probabilities.
Settle	Settlement date is a serial date number or date character vector. Settle must be earlier than the maturity date.
OptionMaturity	N-by-1 vector of serial date numbers or date character vectors containing the option maturity dates.
CDSMaturity	N-by-1 vector of serial date numbers or date character vectors containing the CDS maturity dates.
Strike	N-by-1 vector of option strikes expressed in basis points.
SpreadVol	N-by-1 vector of annualized credit spread volatilities expressed as a positive decimal number.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is 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 Name1,Value1,...,NameN,ValueN.

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.

'AdjustedForwardSpread'	N-by-1 vector of adjusted forward spreads (in basis points) to be used when pricing CDS index options. Default: unadjusted forward spread normally used for single-name CDS options
'Basis'	N-by-1 vector of contract day-count basis: 0 = actual/actual 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (BMA) 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. Default: 2 (actual/360)
'BusDayConvention'	Business day conventions, specified by 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. Default: actual
'Knockout'	N-by-1 vector of Boolean flags. If the credit default swaptions is a knockout, the flag is True, otherwise it is False. Default: False
'PayAccruedPremium'	N-by-1 vector of Boolean flags. If accrued premiums are paid upon default, the flag is True, otherwise it is False. Default: True
'Period'	N-by-1 vector of the number of premiums per year of the CDS. Allowed values are 1, 2, 3, 4, 6, and 12. Default: 4
'RecoveryRate'	N-by-1 vector of recovery rates, expressed as a decimal from 0 to 1. Default: 0.4
'ZeroBasis'	Basis of the zero curve. Choices are identical to Basis. Default: 0 (actual/actual)
'ZeroCompounding'	Compounding frequency of the zero curve. Allowed values are: 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. Default: 2 (Semiannual compounding)

Output Arguments

Payer	N-by-1 vector of prices for payer swap options in Basis points.
Receiver	N-by-1 vector of prices for receiver swap options in Basis points.

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

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]:

$$V_{Pay(Knockout)}=RPV01(t,t_E,T)(F\Phi (d_1)-K\Phi (d_2))$$

$$V_{Rec(Knockout)}=RPV01(t,t_E,T)(K\Phi (-d_2)-F\Phi (-d_1))$$

$$d_1=\frac{\ln \left(\frac{F}{K}\right)+\frac{1}{2}{\sigma }^2(t_E-t)}{\sigma \sqrt{t_E-t}}$$

$$d_2=d_1-\sigma \sqrt{t_E-t}$$

$$V_{Pay(Non-Knockout)}=V_{Pay(Knockout)}+FEP$$

$$V_{Pay(Non-Knockout)}=V_{Rec(Knockout)}$$

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.

t_E 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.