Financial Derivatives Toolbox    
swapbyhjm

Price swap by HJM interest rate tree

Syntax

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.

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.

Use swapbyhjm to compute the price of the swap.

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.

See Also

capbyhjm, cfbyhjm, floorbyhjm, hjmtree


 ratetimes swapbyzero