Financial Derivatives Toolbox™

swapbyhjm - Price swap instrument from HJM interest-rate tree

Syntax

[Price, PriceTree, CFTree, SwapRate] = swapbyhjm(HJMTree,
LegRate, Settle, Maturity, LegReset, Basis, Principal,
LegType)

Arguments

The Settle date for every swap is set to the ValuationDate of the HJM tree. The swap argument Settle is ignored.

This function also calculates the SwapRate (fixed rate) so that the value of the swap is initially zero. To do this enter CouponRate as NaN.

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 swaps' 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.

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 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 

Price the swap using the HJMTree included in the MAT-file deriv.mat. The HJMTree structure contains the time and forward-rate information needed to price the instrument.

load deriv.mat; 

Use swapbyhjm to compute the price of the swap.

[Price, PriceTree, CFTree] = swapbyhjm(HJMTree, LegRate,... 
Settle, Maturity, LegReset, Basis, Principal, LegType) 

Price = 

   3.6923 

PriceTree = 

    FinObj: 'HJMPriceTree'
      tObs: [0 1 2 3 4]
     PBush: {1x5 cell}

CFTree = 

    FinObj: 'HJMCFTree'
      tObs: [0 1 2 3 4]
    CFBush: {[0] [1x1x2 double] [1x2x2 double] ... [1x8 double]}

Using the function treeviewer, you can examine CFTree graphically and see the cash flows from the swap along both the up and the down branches. A positive cash flow indicates an inflow (income - payments > 0), while a negative cash flow indicates an outflow (income - payments < 0).

treeviewer(CFTree)

Note   treeviewer price tree diagrams follow the convention that increasing prices appear on the upper branch of a tree and, consequently, decreasing prices appear on the lower branch. Conversely, for interest-rate displays, decreasing interest rates appear on the upper branch (prices are rising) and increasing interest rates on the lower branch (prices are falling).

In this example, you have sold a swap (receive fixed rate and pay floating rate). At time t = 3, if interest rates go down, your cash flow is positive ($2.63), meaning that you will receive this amount. But if interest rates go up, your cash flow is negative (-$1.58), meaning that you owe this amount.

Example 2. 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, PriceTree, CFTree, SwapRate] = swapbyhjm(HJMTree,... 
LegRate, Settle, Maturity, LegReset, Basis, Principal, LegType) 

Price = 

   0

PriceTree = 

FinObj: 'HJMPriceTree' 
  tObs: [0 1 2 3 4] 
 PBush:{[0] [1x1x2 double] [1x2x2 double] ... [1x8 double]}

CFTree = 

FinObj: 'HJMCFTree' 
  tObs: [0 1 2 3 4] 
CFBush:{[0] [1x1x2 double] [1x2x2 double] ... [1x8 double]}

SwapRate = 

   0.0466

See Also

capbyhjm, cfbyhjm, floorbyhjm, hjmtree

swapbybk

swapbyhw