# floorbybk

Price floor instrument from Black-Karasinski interest-rate tree

## Description

example

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

example

[Price,PriceTree] = floorbybk(___,Reset,Basis,Principal,Options) adds optional arguments.

## Examples

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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 floor instrument.

Set the required values. Other arguments will use defaults.

Strike = 0.03;
Settle = '01-Jan-2004';
Maturity = '01-Jan-2007';

Use floorbybk to compute the price of the floor instrument.

Price = floorbybk(BKTree, Strike, Settle, Maturity)
Price = 0.2061

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

Settle = '01-Jan-2004';
Maturity = '01-Jan-2008';
Strike = 0.045;
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 floors.

Basis = 1;
Price = floorbybk(BKTree, Strike, Settle, Maturity, Reset, Basis, Principal)
Price = 2×1

2.2000
2.5564

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

Data Types: double | char | cell

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

Data Types: double | char | cell

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

Data Types: double

(Optional) 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

Data Types: double

(Optional) 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 floor.

Data Types: double | cell

(Optional) Derivatives pricing options structure, specified using derivset.

Data Types: struct

## Output Arguments

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

Tree structure with values of the floor 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.PTree contains floor prices.

• PriceTree.tObs contains the observation times.

• PriceTree.Connect contains the connectivity vectors. Each element in the cell array describes how nodes in that level connect to the next. For a given tree level, there are NumNodes elements in the vector, and they contain the index of the node at the next level that the middle branch connects to. Subtracting 1 from that value indicates where the up-branch connects to, and adding 1 indicated where the down branch connects to.

• PriceTree.Probs contains the probability arrays. Each element of the cell array contains the up, middle, and down transition probabilities for each node of the level.

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### Floor

A floor is a contract that includes a guarantee setting the minimum interest rate to be received by the holder, based on an otherwise floating interest rate.

The payoff for a floor is:

$\mathrm{max}\left(FloorRate-CurrentRate,0\right)$

Introduced before R2006a