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capbybdt

Price cap instrument from Black-Derman-Toy 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) 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 (BMA)

  • 5 = 30/360 (ISDA)

  • 6 = 30/360 (European)

  • 7 = actual/365 (Japanese)

  • 8 = actual/actual (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/actual (ISDA)

  • 13 = BUS/252

For more information, see basis.

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

expand all

Price a 3% Cap Instrument Using a BDT Interest-Rate Tree

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

load deriv.mat;

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 =

   28.4001

Price a 10% Cap Instrument Using a BDT Interest-Rate Tree

Set the required arguments for the three specifications required to create a BDT tree.

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];

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);

Create the BDT tree from the specifications.

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

      FinObj: 'BDTFwdTree'
     VolSpec: [1x1 struct]
    TimeSpec: [1x1 struct]
    RateSpec: [1x1 struct]
        tObs: [0 1 2 3 4]
        dObs: [730486 730852 731217 731582 731947]
        TFwd: {[5x1 double]  [4x1 double]  [3x1 double]  [2x1 double]  [4]}
      CFlowT: {[5x1 double]  [4x1 double]  [3x1 double]  [2x1 double]  [5]}
     FwdTree: {1x5 cell}

Set the cap arguments. Remaining arguments will use defaults.

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

Use capbybdt to find the price of the cap instrument.

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

    1.7169

See Also

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