Financial Derivatives Toolbox

swapbybdt

Price swap instrument by BDT interest rate tree

Syntax

• [Price, PriceTree, CFTree, SwapRate] = swapbybdt(BDTTree, LegRate, 
  Settle, Maturity, LegReset, Basis, Principal, LegType, Options)
  

Arguments

BDTTree	Interest rate tree structure created by bdttree.
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 BDT 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] = swapbybdt(BDTTree, LegRate, Settle, Maturity, LegReset, Basis, Principal, LegType) computes the price of a swap instrument from a BDT 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. 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:

• Coupon rate for fixed leg: 0.15 (15%)
• Spread for floating leg: 10 basis points
• Swap settlement date: Jan. 01, 2000
• Swap maturity date: Jan. 01, 2003

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 = [0.15 10]; % [CouponRate Spread] 
  LegType = [1 0]; % [Fixed Float] 
  LegReset = [1 1]; % Payments once per year 
  

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

• load deriv; 
  

Use swapbybdt to compute the price of the swap.

• Price  = swapbybdt(BDTTree, LegRate, Settle, Maturity,... 
  LegReset, Basis, Principal, LegType) 
  
  Price =
  
    7.3032
  

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] = swapbybdt(BDTTree,... 
  LegRate, Settle, Maturity, LegReset, Basis, Principal, LegType) 
  
  Price =
  
   -2.8422e-014
  
  PriceTree = 
  
      FinObj: 'BDTPriceTree'
        tObs: [0 1 2 3 4]
       PTree: {1x5 cell}
  
  CFTree = 
  
      FinObj: 'BDTCFTree'
        tObs: [0 1 2 3 4]
      CFTree: {1x5 cell}
  
  SwapRate =
  
      0.1210
  

Example 3.

Calculate the cash flows from a pair of swaps and display the result.

• Settle = '01-Jan-2000';
  Maturity = '01-Jan-2003';
  Basis = 0; 
  Principal = 100;
  LegRate= [0.15 10; 0.15 0]; % [CouponRate Spread] 
  LegType = [1 0; 1 0];
  LegReset = [1 1; 1 1]; 
  
  load deriv 
  
  [Price, PriceTree, CFTree, SwapRate] = swapbybdt(BDTTree,... 
  LegRate, Settle, Maturity, LegReset, Basis, Principal, LegType);
  

Continuing on, provide names for the swaps. Then use treeviewer to observe the cash flow data graphically.

• Names ={'Swap1', 'Swap2'};
  treeviewer(CFTree, Names)
  
  
  

You can use treeviewer to display cash flow data at all observation times and along all branches of the tree.

See Also

bdttree, capbybdt, cfbybdt, floorbybdt

ratetimes

swapbyhjm