swapbyzero - Price swap instrument from set of zero curves

Syntax

[Price, SwapRate AI, RecCF, RecCFDates, PayCF, PayCFDates] = swapbyzero(RateSpec, LegRate, Settle, Maturity) [Price, SwapRate, AI, RecCF, RecCFDates, PayCF, PayCFDates] = swapbyzero(RateSpec, LegRate, Settle, Maturity, Name, Value)

Description

[Price, SwapRate AI, RecCF, RecCFDates, PayCF, PayCFDates] =swapbyzero(RateSpec, LegRate, Settle, Maturity) prices a swap instrument from a set of zero coupon bond rates. All inputs are either scalars or NINST-by-1 vectors unless otherwise specified. Any date can be a serial date number or date string. An optional argument can be passed as an empty matrix [].

[Price, SwapRate, AI, RecCF, RecCFDates, PayCF, PayCFDates] = swapbyzero(RateSpec, LegRate, Settle, Maturity, Name, Value) prices a swap instrument from a set of zero coupon bond rates with additional options specified by one or more Name, Value pair arguments.

Input Arguments

`RateSpec`	Structure containing the properties of an interest-rate structure. See `intenvset` for information on creating `RateSpec`. `RateSpec` can be a `NINST`-by-`2` input variable of `RateSpec`s, with the second input being the discount curve for the paying leg if different than the receiving leg. If only one curve is specified, than it is used to discount both legs.
`LegRate`	Number of instruments (`NINST`)-by-`2` matrix, with each row defined as: `[CouponRate Spread]` or `[Spread CouponRate]` `CouponRate` is the decimal annual rate. `Spread` is the number of basis points over the reference rate. The first column represents the receiving leg, while the second column represents the paying leg.
`Settle`	Settlement date. `NINST`-by-`1` vector of serial date numbers or date strings representing the settlement date for each swap. `Settle` must be earlier than `Maturity`.
`Maturity`	Maturity date. `NINST`-by-`1` vector of dates representing the maturity date for each swap.

Name-Value Pair Arguments

Optional comma-separated pairs of Name,Value arguments, where Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,…,NameN,ValueN.

Note You can either use LegReset, Basis, Principal, LegType, and EndMonthRule as name-value pair arguments in any order, or you can specify these as optional input arguments in the following order: [Price, SwapRate AI, RecCF, RecCFDates, PayCF, PayCFDates] = swapbyzero(RateSpec, LegRate, Settle, Maturity, LegReset, Basis, Principal, LegType, EndMonthRule). The ordered optional input syntax and name value pair syntax cannot be combined.

AdjustCashFlowsBasis

Adjust the cash flows based on the actual period day count. NINST-by-1 of logicals.
Default: False
Basis

Day-count basis of the instrument. A vector of integers.
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/actual (ISDA)
13 = BUS/252

Basis can be a NINST-by-2 input variable of scalars, with the second input being the basis for the paying leg if different than the receiving leg. If only one basis is specified, then it is used for both legs. For more information, see basis.

Default: 0 (actual/actual)
BusinessDayConvention

Require payment dates to be business dates. NINST-by-1 cell array with possible choices for business day convention:
actual
follow
modifiedfollow
previous
modifiedprevious
Default: actual
EndMonthRule

NINST-by-1 vector representing the End-of-month rule.
Default: 1
ForwardRateSpec

Forward rate spec to use in generating cash flows.

Default: If not specified, then the RateSpec is used both for discounting cash flows and generating floating cash flows.
Holidays

Holidays used for business day convention. A NHOLIDAYS-by-1 of MATLAB date numbers.
Default: If none specified, holidays.m is used.
LatestFloatingRate

Rate for the next floating payment, set at the last reset date. NINST-by-1 of scalars.
Default: If not specified, then the RateSpec must contain this information.
LegReset

(Optional) NINST-by-2 matrix representing the reset frequency per year for each swap.

Default: [1 1]
LegType

NINST-by-2 matrix. Each row represents an instrument. Each column indicates if the corresponding leg is fixed (1) or floating (0). This matrix defines the interpretation of the values entered in LegRate.

Default: [1 0] for each instrument
Principal

(Optional) NINST-by-1 vector of the notional principal amounts.

Default: 100

Output Arguments

Price

A number of instruments (NINST) by number of curves (NUMCURVES) matrix of swap prices. Each column arises from one of the zero curves.

SwapRate

A NINST-by-NUMCURVES matrix of rates applicable to the fixed leg such that the swap's values are zero at time 0. This rate is used in calculating the swaps' prices when the rate specified for the fixed leg in LegRate is NaN. The SwapRate output is padded with NaN for those instruments in which CouponRate is not set to NaN.

Output cash flows, cash flow dates, and accrued interest.

AI

NINST-by-NUMCURVES matrix of accrued interest.

RecCF

NINST-by-NUMCURVES matrix of cash flows for the receiving leg.

Note If there is more than one curve specified in the RateSpec input, then the first NCURVES row corresponds to the first bond, the second NCURVES row correspond to the second bond, and so on.

RecCFDates

NINST-by-NUMCURVES matrix of payment dates for the receiving leg.

PayCF

NINST-by-NUMCURVES matrix of cash flows for the fixed leg.

PayCFDates

NINST-by-NUMCURVES matrix of payment dates for the fixed leg.

Examples

Price an interest-rate swap with a fixed receiving leg and a floating paying leg. Payments are made once a year, and the notional principal amount is $100. The values for the remaining arguments are:

Coupon rate for fixed leg: 0.06 (6%)
Spread for floating leg: 20 basis points
Swap settlement date: Jan. 01, 2000
Swap maturity date: Jan. 01, 2003

Based on the information above, set the required arguments and build the LegRate, LegType, and LegReset matrices:

Settle = '01-Jan-2000';
Maturity = '01-Jan-2003';
Basis = 0; 
Principal = 100;
LegRate = [0.06 20]; % [CouponRate Spread] 
LegType = [1 0]; % [Fixed Float] 
LegReset = [1 1]; % Payments once per year

Load the file deriv.mat, which provides ZeroRateSpec, the interest-rate term structure needed to price the bond:

load deriv.mat;

Use swapbyzero to compute the price of the swap:

Price = swapbyzero(ZeroRateSpec, LegRate, Settle, Maturity,... 
LegReset, Basis, Principal, LegType)

Price = 
   3.6923

Using the previous data, calculate the swap rate, which is the coupon rate for the fixed leg such that the swap price at time = 0 is zero:

LegRate = [NaN 20]; 

[Price, SwapRate] = swapbyzero(ZeroRateSpec, LegRate, Settle,...
Maturity, LegReset, Basis, Principal, LegType) 

Price = 

 -1.4211e-014

SwapRate = 
   0.0466

Use swapbyzero with name-value pair arguments for LegRate, LegType, LatestFloatingRate, AdjustCashFlowsBasis, and BusinessDayConvention to calculate output for Price, SwapRate, AI, RecCF, RecCFDates, PayCF, and PayCFDates:

Settle = datenum('08-Jun-2010');
RateSpec = intenvset('Rates', [.005 .0075 .01 .014 .02 .025 .03]',...
'StartDates',Settle, 'EndDates',{'08-Dec-2010','08-Jun-2011',...
'08-Jun-2012','08-Jun-2013','08-Jun-2015','08-Jun-2017','08-Jun-2020'}');
Maturity = datenum('15-Sep-2020');
LegRate = [.025 50];
LegType = [1 0]; % fixed/floating
LatestFloatingRate = .005;
 
[Price, SwapRate, AI, RecCF, RecCFDates, PayCF,PayCFDates] = ...
swapbyzero(RateSpec, LegRate, Settle, Maturity,'LegType',LegType,...
'LatestFloatingRate',LatestFloatingRate,'AdjustCashFlowsBasis',true,...
'BusinessDayConvention','modifiedfollow')

Price =

   -3.3937

SwapRate =

   NaN

AI =

    1.4575


RecCF =

Columns 1 through 10

-1.8219    1.2603    1.2603    1.2740    1.2671   1.2466    1.2534    1.2603   1.2603  1.2740

Columns 11 through 12

1.2671  101.2534


RecCFDates =

Columns 1 through 8

734297      734396      734761     735129     735493      735857    736222   736588

Columns 9 through 12

736953      737320      737684      738049


PayCF =

Columns 1 through 10

-0.3644    0.2521    0.7082    1.0116    1.4423    1.6380   1.9161    2.1038  2.2768  2.2766

Columns 11 through 12

2.4370  102.3432


PayCFDates =

Columns 1 through 8

734297      734396      734761      735129      735493      735857    736222     736588

Columns 9 through 12

736953      737320      737684      738049

Search MATLAB Documentation
R2011b Documentation → Financial Derivatives Toolbox
View documentation for other releases	Learn more about Financial Derivatives Toolbox

`AdjustCashFlowsBasis`	Adjust the cash flows based on the actual period day count. `NINST`-by-`1` of logicals. Default: `False`
`Basis`	Day-count basis of the instrument. A vector of integers. 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/actual (ISDA) 13 = BUS/252 `Basis` can be a `NINST`-by-`2` input variable of scalars, with the second input being the basis for the paying leg if different than the receiving leg. If only one basis is specified, then it is used for both legs. For more information, see basis. Default: `0` (actual/actual)
`BusinessDayConvention`	Require payment dates to be business dates. `NINST`-by-`1` cell array with possible choices for business day convention: `actual` `follow` `modifiedfollow` `previous` `modifiedprevious` Default: `actual`
`EndMonthRule`	`NINST`-by-`1` vector representing the End-of-month rule. Default: `1`
`ForwardRateSpec`	Forward rate spec to use in generating cash flows. Default: If not specified, then the `RateSpec` is used both for discounting cash flows and generating floating cash flows.
`Holidays`	Holidays used for business day convention. A `NHOLIDAYS`-by-`1` of MATLAB date numbers. Default: If none specified, `holidays.m` is used.
`LatestFloatingRate`	Rate for the next floating payment, set at the last reset date. `NINST`-by-`1` of scalars. Default: If not specified, then the `RateSpec` must contain this information.
`LegReset`	(Optional) `NINST`-by-`2` matrix representing the reset frequency per year for each swap. Default: `[1 1]`
`LegType`	`NINST`-by-`2` matrix. Each row represents an instrument. Each column indicates if the corresponding leg is fixed (`1`) or floating (`0`). This matrix defines the interpretation of the values entered in `LegRate`. Default: `[1 0]` for each instrument
`Principal`	(Optional) `NINST`-by-`1` vector of the notional principal amounts. Default: `100`