Documentation

This is machine translation

Translated by Microsoft
Mouseover text to see original. Click the button below to return to the English verison of the page.

Note: This page has been translated by MathWorks. Please click here
To view all translated materals including this page, select Japan from the country navigator on the bottom of this page.

capbybdt

Price cap instrument from Black-Derman-Toy interest-rate tree

Syntax

[Price,PriceTree] = capbybdt(BDTTree,Strike,Settle,Maturity)
[Price,PriceTree] = capbybdt(___Name,Value)

Description

example

[Price,PriceTree] = capbybdt(BDTTree,Strike,Settle,Maturity) computes the price of a cap instrument from a Black-Derman-Toy interest-rate tree. capbybdt computes prices of vanilla caps and amortizing caps.

example

[Price,PriceTree] = capbybdt(___Name,Value) adds optional name-value pair arguments.

Examples

collapse all

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

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 = struct with fields:
      FinObj: 'BDTFwdTree'
     VolSpec: [1×1 struct]
    TimeSpec: [1×1 struct]
    RateSpec: [1×1 struct]
        tObs: [0 1 2 3 4]
        dObs: [730486 730852 731217 731582 731947]
        TFwd: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [4]}
      CFlowT: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [5]}
     FwdTree: {[1.1000]  [1.0979 1.1432]  [1.0976 1.1377 1.1942]  [1.0872 1.1183 1.1606 1.2179]  [1.0865 1.1134 1.1486 1.1948 1.2552]}

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

Define the RateSpec.

Rates = [0.03583; 0.042147; 0.047345; 0.052707; 0.054302];
ValuationDate = '15-Nov-2011';
StartDates = ValuationDate;
EndDates = {'15-Nov-2012';'15-Nov-2013';'15-Nov-2014' ;'15-Nov-2015';'15-Nov-2016'};
Compounding = 1;
RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: 1
             Disc: [5×1 double]
            Rates: [5×1 double]
         EndTimes: [5×1 double]
       StartTimes: [5×1 double]
         EndDates: [5×1 double]
       StartDates: 734822
    ValuationDate: 734822
            Basis: 0
     EndMonthRule: 1

Define the cap instrument.

Settle ='15-Nov-2011';
Maturity = '15-Nov-2015';
Strike = 0.04;
Reset = 1;
Principal ={{'15-Nov-2012' 100;'15-Nov-2013' 70;'15-Nov-2014' 40;'15-Nov-2015' 10}};

Build the BDT Tree.

BDTTimeSpec = bdttimespec(ValuationDate, EndDates);
Volatility = 0.10;  
BDTVolSpec = bdtvolspec(ValuationDate, EndDates, Volatility*ones(1,length(EndDates))');
BDTTree = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec)
BDTTree = struct with fields:
      FinObj: 'BDTFwdTree'
     VolSpec: [1×1 struct]
    TimeSpec: [1×1 struct]
    RateSpec: [1×1 struct]
        tObs: [0 1 2 3 4]
        dObs: [734822 735188 735553 735918 736283]
        TFwd: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [4]}
      CFlowT: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [5]}
     FwdTree: {[1.0358]  [1.0437 1.0534]  [1.0469 1.0573 1.0700]  [1.0505 1.0617 1.0754 1.0921]  [1.0401 1.0490 1.0598 1.0731 1.0894]}

Price the amortizing cap.

Basis = 0;
Price = capbybdt(BDTTree, Strike, Settle, Maturity, Reset, Basis, Principal)
Price = 1.4042

Input Arguments

collapse all

Interest-rate tree structure, specified by using bdttree.

Data Types: struct

Rate at which cap is exercised, specified as a NINST-by-1 vector of decimal values.

Data Types: double

Settlement date for the cap, specified as a NINST-by-1 vector of serial date numbers or date character vectors. The Settle date for every cap is set to the ValuationDate of the BDT tree. The cap argument Settle is ignored.

Data Types: double | char | cell

Maturity date for the cap, specified as a NINST-by-1 vector of serial date numbers or date character vectors.

Data Types: double | char | cell

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: [Price,PriceTree] = capbybdt(BDTTree,Strike,Settle,Maturity,'Reset',4,'Principal',10000,'Basis',5)

collapse all

Reset frequency payment per year, specified as a NINST-by-1 vector.

Data Types: double

Day-count basis representing the basis used when annualizing the input forward rate, specified as a NINST-by-1 vector of integers.

  • 0 = actual/actual

  • 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 (ICMA)

  • 9 = actual/360 (ICMA)

  • 10 = actual/365 (ICMA)

  • 11 = 30/360E (ICMA)

  • 12 = actual/365 (ISDA)

  • 13 = BUS/252

For more information, see basis.

Data Types: double

Notional principal amount, specified as a NINST-by-1 of notional principal amounts, or a NINST-by-1 cell array, where each element is a NumDates-by-2 cell array where the first column is dates and the second column is associated principal amount. The date indicates the last day that the principal value is valid.

Use Principal to pass a schedule to compute the price for an amortizing cap.

Data Types: double | cell

Derivatives pricing options structure, specified using derivset.

Data Types: struct

Output Arguments

collapse all

Expected price of the cap at time 0, returned as a NINST-by-1 vector.

Tree structure with values of the cap at each node, returned as a MATLAB® structure of trees containing vectors of instrument prices and a vector of observation times for each node:

  • PriceTree.tObs contains the observation times.

Introduced before R2006a

Was this topic helpful?