Financial Derivatives Toolbox™

floorbybdt - Price floor instrument from 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) Day-count basis of the instrument. A vector of integers. 0 = actual/actual (default) 1 = 30/360 (SIA) 2 = actual/360 3 = actual/365 4 = 30/360 (PSA) 5 = 30/360 (ISDA) 6 = 30/360 (European) 7 = actual/365 (Japanese) 8 = actual/actual (ISMA) 9 = actual/360 (ISMA) 10 = actual/365 (ISMA) 11 = 30/360E (ISMA) 12 = actual/365 (ISDA)
`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.mat;

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. Remaining arguments will use defaults.

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

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

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

Price =

    0.0431

floorbybdt - Price floor instrument from BDT interest-rate tree

Syntax

Arguments

Description

Examples

See Also