floorbybk

Price floor instrument from Black-Karasinski interest-rate tree

Syntax

[Price,PriceTree] = floorbybk(BKTree,Strike,Settle,Maturity)

[Price,PriceTree] = floorbybk(___,Reset,Basis,Principal,Options)

Description

[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.

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

Examples

Price a 3% Floor 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 floor 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 floorbybk to compute the price of the floor instrument.

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

Price = 0.2061

Compute the Price of an Amortizing and Vanilla Floors Using the BK Model

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

load deriv.mat; 
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

BKTree — Interest-rate tree structure

structure

Interest-rate tree structure, specified by using bktree.

Data Types: struct

Strike — Rate at which cap is exercised

decimal

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

Data Types: double

Settle — Settlement date for floor

serial date number | date character vector | cell array of date character vectors

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 — Maturity date for floor

serial date number | date character vector | cell array of date character vectors

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

Reset — Reset frequency payment per year

1 (default) | numeric

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

Data Types: double

Basis — Day-count basis of instrument

0 (actual/actual) (default) | integer from 0 to 13

(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

For more information, see Basis.

Data Types: double

Principal — Notional principal amount

100 (default) | numeric

(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

Options — Derivatives pricing options structure

structure

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

Data Types: struct

Output Arguments

Price — Expected price of floor at time 0

vector

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

PriceTree — Tree structure with values of floor at each node

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.

More About

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:

$$\max (FloorRate-CurrentRate,0)$$