Financial Derivatives Toolbox

floorbybdt

Price floor instrument by BDT interest rate tree

Syntax

• [Price, PriceTree] = floorbybdt(BDTTree, Strike, Settle, Maturity, 
  Reset, Basis, Principal, Options)
  

Arguments

BDTTree	Interest rate tree structure created by bdttree.
Strike	Number of instruments (NINST)-by-1 vector of rates at which the floor is exercised.
Settle	Settlement date. NINST-by-1 vector of dates representing the settlement dates of the floor. The Settle date for every floor is set to the ValuationDate of the BDT tree. The floor argument Settle is ignored.
Maturity	NINST-by-1 vector of dates representing the maturity dates of the floor.
Reset	(Optional) NINST-by-1 vector representing the frequency of payments per year. Default = 1.
Basis	(Optional) NINST-by-1 vector representing the basis used when annualizing the input forward rate tree. Default = 0 (actual/actual).
Principal	(Optional) The notional principal amount. Default = 100.
Options	(Optional) Derivatives pricing options structure created with derivset.

Description

[Price, PriceTree] = floorbybdt(BDTTree, Strike, Settlement, Maturity, Reset, Basis, Principal, Options) computes the price of a floor instrument from a BDT interest rate tree.

Price is an NINST-by-1 vector of the expected prices of the floor at time 0.

PriceTree is the tree structure with values of the floor at each node.

Examples

Example 1.

Price a 10% floor instrument using a BDT interest rate tree.

Load the file deriv.mat, which provides BDTTree. BDTTree contains the time and interest rate information needed to price the floor instrument.

• load deriv 
  

Set the required values. Other arguments will use defaults.

• Strike = 0.10;
  Settle = '01-Jan-2000';
  Maturity = '01-Jan-2004';
  

Use floorbybdt to compute the price of the floor instrument.

• Price = floorbybdt(BDTTree, Strike, Settle, Maturity)
  
  Price =
  
     0.1770
  

Example 2.

Here is a second example, showing the pricing of a 10% floor instrument using a newly-created BDT tree.

First set the required arguments for the three needed specifications.

• Compounding = 1; 
  ValuationDate = '01-01-2000'; 
  StartDate = ValuationDate; 
  EndDates = ['01-01-2001'; '01-01-2002'; '01-01-2003'; 
  '01-01-2004'; '01-01-2005']; 
  Rates = [.1; .11; .12; .125; .13]; 
  Volatility = [.2; .19; .18; .17; .16];
  

Next create the specifications.

• RateSpec = intenvset('Compounding', Compounding,... 
  'ValuationDate', ValuationDate,... 
  'StartDates', StartDate,... 
  'EndDates', EndDates,... 
  'Rates', Rates); 
  BDTTimeSpec = bdttimespec(ValuationDate, EndDates, Compounding); 
  BDTVolSpec = bdtvolspec(ValuationDate, EndDates, Volatility); 
  

Now create the BDT tree from the specifications.

• BDTTree = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec);
  

Set the floor arguments.

• FloorStrike = 0.10; 
  Settlement = ValuationDate; 
  Maturity = '01-01-2002'; 
  FloorReset = 1;
  

Remaining arguments will use defaults.

Finally, use floorbybdt to find the price of the floor instrument.

• Price= floorbybdt(BDTTree, FloorStrike, Settlement, Maturity,... 
  FloorReset) 
  
  Price =
  
      0.0431
  

See Also

bdttree, capbybdt, cfbybdt, swapbybdt

floatbyzero

floorbyhjm