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Price cap instrument from Black-Karasinski interest-rate tree


[Price,PriceTree] = capbybk(BKTree,Strike,Settle,Maturity)
[Price,PriceTree] = capbybk(___Name,Value)



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


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


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Load the file deriv.mat, which provides BKTree. The BKTree 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-2004';
Maturity = '01-Jan-2007';

Use capbybk to compute the price of the cap instrument.

Price = capbybk(BKTree, Strike, Settle, Maturity)
Price = 2.0965

Load deriv.mat to specify the BKTree and then define the cap instrument.

load deriv.mat; 
Settle = '01-Jan-2004';
Maturity = '01-Jan-2008';
Strike = 0.05;
Reset = 1;
Principal ={{'01-Jan-2005' 100;'01-Jan-2006' 60;'01-Jan-2007' 30;'01-Jan-2008' 30};...

Price the amortizing and vanilla caps.

Basis = 1;
Price = capbybk(BKTree, Strike, Settle, Maturity, Reset, Basis, Principal)
Price = 


Input Arguments

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Interest-rate tree structure, specified by using bktree.

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 BK 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] = capbybk(BKTree,Strike,Settle,Maturity,'Reset',4,'Principal',10000,'Basis',5)

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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

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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

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