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# capbybk

Price cap instrument from Black-Karasinski interest-rate tree

## Syntax

[Price, PriceTree] = capbybk(BKTree, Strike, Settle, Maturity,
Reset, Basis, Principal, Options)

## Arguments

 BKTree Interest-rate tree structure created by bktree. 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/3603 = actual/3654 = 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/252For more information, see basis. Principal (Optional) NINST-by-1 of notional principal amounts or 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. Default is 100. Options (Optional) Derivatives pricing options structure created with derivset.

## Description

[Price, PriceTree] = capbybk(BKTree, Strike, Settle, Maturity,
Reset, Basis, Principal, Options)
computes the price of a cap instrument from a Black-Karasinski 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 BK tree. The cap argument Settle is ignored.

 Note:   Use the optional name-value pair argument, Principal, to pass a schedule to compute price for an amortizing cap.

## Examples

expand all

### Price a 3% Cap Instrument Using a Black-Karasinski Interest-Rate Tree

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

```

### Compute the Price of an Amortizing and Vanilla Caps Using the BK Model

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};...
100};
```

Price the amortizing and vanilla caps.

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

0.2226
0.7422

```