floorbyhw
Price floor instrument from Hull-White interest-rate tree
Syntax
Description
Examples
Price a 3% Floor Instrument Using a Hull-White Interest-Rate Tree
Load the file deriv.mat
, which provides HWTree
. The HWTree
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 floorbyhw
to compute the price of the floor instrument.
Price = floorbyhw(HWTree, Strike, Settle, Maturity)
Price = 0.4186
Compute the Price of an Amortizing and Vanilla Floors Using the HW Model
Define the RateSpec
.
Rates = [0.035; 0.042; 0.047; 0.052; 0.054]; ValuationDate = '01-April-2014'; StartDates = ValuationDate; EndDates = {'01-April-2019'}; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,... 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RateSpec = struct with fields:
FinObj: 'RateSpec'
Compounding: 1
Disc: [5x1 double]
Rates: [5x1 double]
EndTimes: [5x1 double]
StartTimes: [5x1 double]
EndDates: 737516
StartDates: 735690
ValuationDate: 735690
Basis: 0
EndMonthRule: 1
Define the floor instruments.
Settle ='01-April-2014'; Maturity = '01-April-2018'; Strike = 0.05; FloorReset = 1; Principal ={{'01-April-2015' 100;'01-April-2016' 60;'01-April-2017' 40;'01-April-2018' 20}; 100};
Build the HW Tree.
VolDates = ['01-April-2015';'01-April-2016';'01-April-2017';'01-April-2018']; VolCurve = 0.05; AlphaDates = '01-April-2018'; AlphaCurve = 0.10; HWVolSpec = hwvolspec(RateSpec.ValuationDate, VolDates, VolCurve,... AlphaDates, AlphaCurve); HWTimeSpec = hwtimespec(RateSpec.ValuationDate, VolDates, Compounding); HWTree = hwtree(HWVolSpec, RateSpec, HWTimeSpec)
HWTree = struct with fields:
FinObj: 'HWFwdTree'
VolSpec: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 struct]
tObs: [0 1 2 3]
dObs: [735690 736055 736421 736786]
CFlowT: {[4x1 double] [3x1 double] [2x1 double] [4]}
Probs: {[3x1 double] [3x3 double] [3x5 double]}
Connect: {[2] [2 3 4] [2 3 4 5 6]}
FwdTree: {1x4 cell}
Price the amortizing and vanilla floors.
Basis = 0; Price = floorbyhw(HWTree, Strike, Settle, Maturity, FloorReset, Basis, Principal)
Price = 2×1
4.8675
10.3881
Input Arguments
HWTree
— Interest-rate tree structure
structure
Interest-rate tree structure, specified by using hwtree
.
Data Types: struct
Strike
— Rate at which floor is exercised
decimal
Rate at which the floor 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 HW 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
FloorReset
— 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 areNumNodes
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:
Version History
See Also
capbyhw
| cfbyhw
| hwtree
| swapbyhw
| floorbynormal
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