# floorbyhjm

Price floor instrument from Heath-Jarrow-Morton interest-rate tree

## Description

example

[Price,PriceTree] = floorbyhjm(HJMTree,Strike,Settle,Maturity) computes the price of a floor instrument from a Heath-Jarrow-Morton interest-rate tree. floorbyhjm computes prices of vanilla floors and amortizing floors.

example

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

## Examples

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This example shows how to price a 3% floor instrument using an HJM forward-rate tree by loading the file deriv.mat, which provides HJMTree. The HJMTree structure contains the time and forward-rate information needed to price the floor instrument.

Strike = 0.03;
Settle = datetime(2000,1,1);
Maturity = datetime(2004,1,1);

Price = floorbyhjm(HJMTree, Strike, Settle, Maturity)
Price = 0.0486

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

Settle = datetime(2000,1,1);
Maturity = datetime(2004,1,1);
Strike = 0.05;
FloorReset = 1;
Principal ={{datetime(2001,1,1) 100;datetime(2002,1,1) 80;datetime(2003,1,1) 70;datetime(2004,1,1) 30}};

Price the amortizing floor.

Price = floorbyhjm(HJMTree, Strike, Settle, Maturity, FloorReset, Principal)
Price = 2.8215

## Input Arguments

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Interest-rate tree structure, specified by using hjmtree.

Data Types: struct

Rate at which the floor 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 using a datetime array, string array, or date character vectors. The Settle date for every floor is set to the ValuationDate of the HJM tree. The floor argument Settle is ignored.

To support existing code, floorbyhjm also accepts serial date numbers as inputs, but they are not recommended.

Maturity date for the floor, specified as a NINST-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, floorbyhjm also accepts serial date numbers as inputs, but they are not recommended.

(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.tObs contains the observation times.

• PriceTree.PBush contains the clean prices.

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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:

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

## Version History

Introduced before R2006a

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