capbybdt (Financial Derivatives Toolbox)

Price cap instrument by BDT interest rate tree

Syntax

[Price, PriceTree] = capbybdt(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 cap is exercised.

Settle
Settlement dates. NINST-by-1 vector of dates representing the settlement dates of the cap.

Maturity
NINST-by-1 vector of dates representing the maturity dates of the cap.

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.

`BDTTree`	Interest rate tree structure created by `bdttree`.
`Strike`	Number of instruments (`NINST`)-by-`1` vector of rates at which the cap is exercised.
`Settle`	Settlement dates. `NINST`-by-`1` vector of dates representing the settlement dates of the cap.
`Maturity`	`NINST`-by-`1` vector of dates representing the maturity dates of the cap.
`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] = capbybdt(BDTTree, Strike, Settle, Maturity, Reset, Basis, Principal, Options) computes the price of a cap instrument from a BDT interest rate tree.

Price is the expected price of the cap at time 0.

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

The Settle date for every cap is set to the ValuationDate of the BDT tree. The cap argument Settle is ignored.

Examples

Example 1.

Price a 3% cap 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 cap instrument.

```
load deriv 
```

Set the required values. Other arguments will use defaults.

Strike = 0.03;
Settle = '01-Jan-2000';
Maturity = '01-Jan-2004';

Use capbybdt to compute the price of the cap instrument.

Price = capbybdt(BDTTree, Strike, Settle, Maturity)

Price =

  28.5191

Example 2.

Here is a second example, showing the pricing of a 10% cap 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 cap arguments.

CapStrike = 0.10; 
Settlement = ValuationDate; 
Maturity = '01-01-2002'; 
CapReset = 1;

Remaining arguments will use defaults.

Finally, use capbybdt to find the price of the cap instrument.

Price= capbybdt(BDTTree, CapStrike, Settlement, Maturity,... 
CapReset)

Price =

    1.6923

bushshape capbyhjm