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Price swap by HJM interest rate tree
Syntax
[Price, PriceTree, CFTree, SwapRate] = swapbyhjm(HJMTree, LegRate, Settle, Maturity, LegReset, Basis, Principal, LegType, Options)
Arguments
HJMTree |
Forward rate tree structure created by hjmtree . |
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. Settle must be earlier than or equal to Maturity . |
Maturity |
Maturity date. NINST -by-1 vector of dates representing the maturity date for each swap. |
LegReset |
(Optional) NINST -by-2 matrix representing the reset frequency per year for each swap. Default = [1 1] . |
Basis | (Optional) NINST -by-1 vector representing the basis used when annualizing the input forward rate tree. Default = 0 (actual/actual). |
Principal |
(Optional) NINST -by-1 vector of the notional principal amounts. Default = 100 . |
LegType |
(Optional) 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 is [1,0] for each instrument. |
Options |
(Optional) Derivatives pricing options structure created with derivset . |
The Settle
date for every swap is set to the ValuationDate
of the HJM tree. The swap argument Settle
is ignored.
Description
[Price, PriceTree, CFTree, SwapRate] = swapbyhjm(HJMTree, LegRate,
Settle, Maturity, LegReset, Basis, Principal, LegType)
computes the price of a swap instrument from an HJM interest rate tree.
Price
is number of instruments (NINST
)-by-1
expected prices of the swap at time 0.
PriceTree
is the tree structure with a vector of the swap values at each node.
CFTree
is the tree structure with a vector of the swap cash flows at each node.
SwapRate
is a NINST
-by-1
vector 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 swap's prices when the rate specified for the fixed leg in LegRate
is NaN
. SwapRate
is padded with NaN
for those instruments in which CouponRate
is not set to NaN
.
Examples
Example 1: 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 parameters are:
Based on the information above, set the required parameters and build the LegRate
, LegType
, and LegReset
matrices.
Settle = '01-Jan-2000'; Maturity = '01-Jan-2003'; Basis = 0; Principal = 100; LegRate = [0.04 20]; % [CouponRate Spread] LegType = [1 0]; % [Fixed Float] LegReset = [1 1]; % Payments once per year
Price the swap using the HJMTree
included in the MAT-file deriv.mat
. HJMTree
contains the time and forward rate information needed to price the instrument.
load deriv
Use swapbyhjm
to compute the price of the swap.
Price = swapbyhjm(HJMTree, LegRate, Settle, Maturity,... LegReset, Basis, Principal, LegType) Price = 5.1910
Example 2: Using the previous data, calculate the swap rate, the coupon rate for the fixed leg such that the swap price at time = 0 is zero.
LegRate = [NaN 20]; [Price, PriceTree, CFTree, SwapRate] = swapbyhjm(HJMTree,... LegRate, Settle, Maturity, LegReset, Basis, Principal, LegType) Price = -1.4211e-014 PriceTree = FinObj: 'HJMPriceTree' tObs: [0 1 2 3 4] PBush: {1x5 cell} CFTree = FinObj: 'HJMCFTree' tObs: [0 1 2 3 4] CFBush: {1x5 cell} SwapRate = 0.0220
See Also
capbyhjm
, cfbyhjm
, floorbyhjm
, hjmtree
![]() | ratetimes | swapbyzero | ![]() |