floatbycir

Price floating-rate note from Cox-Ingersoll-Ross interest-rate tree

Syntax

[Price,PriceTree] = floatbycir(CIRTree,Spread,Settle,Maturity)

[Price,PriceTree] = floatbycir(___,Name,Value)

Description

[Price,PriceTree] = floatbycir(CIRTree,Spread,Settle,Maturity)价格floating-rate note from a Cox-Ingersoll-Ross (CIR) interest-rate tree.

floatbycircomputes prices of vanilla floating-rate notes, amortizing floating-rate notes, capped floating-rate notes, floored floating-rate notes, and collared floating-rate notes using a CIR++ model with the Nawalka-Beliaeva (NB) approach.

example

[Price,PriceTree] = floatbycir(___,Name,Value)adds additional name-value pair arguments.

Examples

collapse all

Price a Floating-Rate Note Using a CIR Interest-Rate Tree

Open Live Script

Define aSpreadof 20-basis points for a floating-rate note.

Spread = 20;

Create aRateSpecusing theintenvsetfunction.

Rates = [0.035; 0.042147; 0.047345; 0.052707]; Dates = {'Jan-1-2017';'Jan-1-2018';'Jan-1-2019';'Jan-1-2020';'Jan-1-2021'}; ValuationDate ='Jan-1-2017'; EndDates = Dates(2:end)'; Compounding = 1; RateSpec = intenvset('ValuationDate', ValuationDate,startdate可以的, ValuationDate,'EndDates',EndDates,'Rates', Rates,'Compounding', Compounding);

Create aCIRtree.

NumPeriods = length(EndDates); Alpha = 0.03; Theta = 0.02; Sigma = 0.1; Settle ='01-Jan-2017'; Maturity ='01-Jan-2021'; CIRTimeSpec = cirtimespec(ValuationDate, Maturity, NumPeriods); CIRVolSpec = cirvolspec(Sigma, Alpha, Theta); CIRT = cirtree(CIRVolSpec, RateSpec, CIRTimeSpec)

CIRT =struct with fields:FinObj: 'CIRFwdTree' VolSpec: [1x1 struct] TimeSpec: [1x1 struct] RateSpec: [1x1 struct] tObs: [0 1 2 3] dObs: [736696 737061 737426 737791] FwdTree: {1x4 cell} Connect: {[3x1 double] [3x3 double] [3x5 double]} Probs: {[3x1 double] [3x3 double] [3x5 double]}

Price the 20-basis point floating-rate note.

[Price,PriceTree] = floatbycir(CIRT,Spread,Settle,Maturity)

Price = 100.7143

PriceTree =struct with fields:FinObj: 'CIRPriceTree' PTree: {1x5 cell} AITree: {[0] [0 0 0] [0 0 0 0 0] [0 0 0 0 0 0 0] [0 0 0 0 0 0 0]} tObs: [0 1 2 3 4] Connect: {[3x1 double] [3x3 double] [3x5 double]} Probs: {[3x1 double] [3x3 double] [3x5 double]}

Input Arguments

collapse all

`CIRTree`—Interest-rate tree structure
structure

Interest-rate tree structure, created bycirtree

Data Types:struct

`Spread`—Number of basis points over the reference rate
vector

Number of basis points over the reference rate, specified as aNINST-by-1vector.

Data Types:double

`Settle`—Settlement date
serial date number|特征向量|string array|datetime

Settlement date, specified either as a scalar orNINST-by-1vector of serial date numbers, date character vectors, string arrays, or datetime arrays.

TheSettledate for every floating-rate note is set to theValuationDateof the CIR tree. The floating-rate note argumentSettleis ignored.

Data Types:char|double|string|datetime

`Maturity`—Maturity date
serial date number|特征向量|string array|datetime

Maturity date, specified as aNINST-by-1vector of serial date numbers, date character vectors, string arrays, or datetime arrays representing the maturity date for each floating-rate note.

Data Types:char|double|string|datetime

Name-Value Arguments

Specify optional comma-separated pairs ofName,Valuearguments.Nameis the argument name andValueis the corresponding value.Namemust appear inside quotes. You can specify several name and value pair arguments in any order asName1,Value1,...,NameN,ValueN.

Example:[Price,PriceTree] = floatbycir(CIRTree,Spread,Settle,Maturity,'Basis',3)

`FloatReset`—Frequency of payments per year
`1`(default) |vector

Frequency of payments per year, specified as the comma-separated pair consisting of'FloatReset'和一个NINST-by-1vector.

Note

Payments on floating-rate notes (FRNs) are determined by the effective interest-rate between reset dates. If the reset period for an FRN spans more than one tree level, calculating the payment becomes impossible due to the recombining nature of the tree. That is, the tree path connecting the two consecutive reset dates cannot be uniquely determined because there is more than one possible path for connecting the two payment dates.

Data Types:double

`Basis`—Day count basis
`0`(实际/实际)(default) |integer from`0`to`13`

Day count basis representing the basis used when annualizing the input forward rate tree, specified as the comma-separated pair consisting of'Basis'和一个NINST-by-1vector.

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, seeBasis.

Data Types:double

`Principal`—Notional principal amounts or principal value schedules
`100`(default) |vector or cell array

Notional principal amounts, specified as the comma-separated pair consisting of'Principal'和一个vector or cell array.

Principalaccepts aNINST-by-1vector orNINST-by-1cell array, where each element of the cell array is aNumDates-by-2cell array, and the first column is dates and the second column is its associated notional principal value. The date indicates the last day that the principal value is valid.

Data Types:cell|double

`EndMonthRule`—End-of-month rule flag for generating dates when`Maturity`is end-of-month date for month having 30 or fewer days
`1`(in effect)(default) |nonnegative integer`[0,1]`

End-of-month rule flag for generating dates whenMaturityis an end-of-month date for a month having 30 or fewer days, specified as the comma-separated pair consisting of'EndMonthRule'和一个nonnegative integer [0,1] using aNINST-by-1vector.

0= Ignore rule, meaning that a payment date is always the same numerical day of the month.
1= Set rule on, meaning that a payment date is always the last actual day of the month.

Data Types:logical

`AdjustCashFlowsBasis`—Flag to adjust cash flows based on actual period day count
`false`(default) |value of`0`(false) or`1`(true)

Flag to adjust cash flows based on actual period day count, specified as the comma-separated pair consisting of'AdjustCashFlowsBasis'和一个NINST-by-1vector of logicals with values of0(false) or1(true).

Data Types:logical

`Holidays`—Holidays used in computing business days
if not specified, the default is to use`holidays.m`(default) |MATLAB^®date numbers

Holidays used in computing business days, specified as the comma-separated pair consisting of'Holidays'and MATLAB date numbers using aNHolidays-by-1vector.

Data Types:double

`BusinessDayConvention`—Business day conventions
`actual`(default) |特征向量|cell array of character vectors

Business day conventions, specified as the comma-separated pair consisting of'BusinessDayConvention'和一个特征向量or aN-by-1cell array of character vectors of business day conventions. The selection for business day convention determines how nonbusiness days are treated. Nonbusiness days are defined as weekends plus any other date that businesses are not open (e.g. statutory holidays). Values are:

actual— Nonbusiness days are effectively ignored. Cash flows that fall on nonbusiness days are assumed to be distributed on the actual date.
follow— Cash flows that fall on a non-business day are assumed to be distributed on the following business day.
modifiedfollow— Cash flows that fall on a non-business day are assumed to be distributed on the following business day. However if the following business day is in a different month, the previous business day is adopted instead.
previous— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day.
modifiedprevious— Cash flows that fall on a non-business day are assumed to be distributed on the previous business day. However if the previous business day is in a different month, the following business day is adopted instead.

Data Types:char|cell

`CapRate`—Annual cap rate
decimal

Annual cap rate, specified as the comma-separated pair consisting of'CapRate'和一个NINST-by-1decimal annual rate orNINST-by-1cell array, where each element is aNumDates-by-2cell array, and the cell array first column is dates, and the second column is associated cap rates. The date indicates the last day that the cap rate is valid.

Data Types:double|cell

`FloorRate`—Annual floor rate
decimal

Annual floor rate, specified as the comma-separated pair consisting of'FloorRate'和一个NINST-by-1decimal annual rate orNINST-by-1cell array.

For theNINST-by-1cell array, each element is aNumDates-by-2cell array, where the cell array first column is dates, and the second column is associated floor rates. The date indicates the last day that the floor rate is valid.

Data Types:double|cell

Output Arguments

collapse all

`Price`预期的浮动利率0时刻注意价格
vector

Expected floating-rate note prices at time 0, returned as aNINST-by-1vector.

`PriceTree`— Tree structure of instrument prices
structure

Tree structure of instrument prices, returned as a MATLAB structure of trees containing vectors of instrument prices and accrued interest, and a vector of observation times for each node. WithinPriceTree:

PriceTree.PTreecontains the clean prices.
PriceTree.AITreecontains the accrued interest.
PriceTree.tObscontains the observation times.
PriceTree.Connectcontains 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 areNumNodeselements 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.Probscontains 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

collapse all

Floating-Rate Note

Afloating-rate noteis a security like a bond, but the interest rate of the note is reset periodically, relative to a reference index rate, to reflect fluctuations in market interest rates.

References

[1] Cox, J., Ingersoll, J.,and S. Ross. "A Theory of the Term Structure of Interest Rates."Econometrica.Vol. 53, 1985.

[2] Brigo, D. and F. Mercurio.Interest Rate Models - Theory and Practice.Springer Finance, 2006.

[3] Hirsa, A.Computational Methods in Finance.CRC Press, 2012.

[4] Nawalka, S., Soto, G., and N. Beliaeva.Dynamic Term Structure Modeling.Wiley, 2007.

[5] Nelson, D. and K. Ramaswamy. "Simple Binomial Processes as Diffusion Approximations in Financial Models."The Review of Financial Studies.Vol 3. 1990, pp. 393–430.

floatbycir

Syntax

Description

Examples

Price a Floating-Rate Note Using a CIR Interest-Rate Tree

Input Arguments

`CIRTree`—Interest-rate tree structure
structure

`Spread`—Number of basis points over the reference rate
vector

`Settle`—Settlement date
serial date number|特征向量|string array|datetime

`Maturity`—Maturity date
serial date number|特征向量|string array|datetime

Name-Value Arguments

`FloatReset`—Frequency of payments per year
`1`(default) |vector

`Basis`—Day count basis
`0`(实际/实际)(default) |integer from`0`to`13`

`Principal`—Notional principal amounts or principal value schedules
`100`(default) |vector or cell array

`EndMonthRule`—End-of-month rule flag for generating dates when`Maturity`is end-of-month date for month having 30 or fewer days
`1`(in effect)(default) |nonnegative integer`[0,1]`

`AdjustCashFlowsBasis`—Flag to adjust cash flows based on actual period day count
`false`(default) |value of`0`(false) or`1`(true)

`Holidays`—Holidays used in computing business days
if not specified, the default is to use`holidays.m`(default) |MATLAB^®date numbers

`BusinessDayConvention`—Business day conventions
`actual`(default) |特征向量|cell array of character vectors

`CapRate`—Annual cap rate
decimal

`FloorRate`—Annual floor rate
decimal

Output Arguments

`Price`预期的浮动利率0时刻注意价格
vector

`PriceTree`— Tree structure of instrument prices
structure

More About

Floating-Rate Note

References

See Also

Topics

Financial Instruments Toolbox Documentation

金宝app

A Practical Guide to Modeling Financial Risk with MATLAB

floatbycir

Syntax

Description

Examples

Price a Floating-Rate Note Using a CIR Interest-Rate Tree

Input Arguments

CIRTree—Interest-rate tree structurestructure

Spread—Number of basis points over the reference ratevector

Settle—Settlement dateserial date number|特征向量|string array|datetime

Maturity—Maturity dateserial date number|特征向量|string array|datetime

Name-Value Arguments

FloatReset—Frequency of payments per year1(default) |vector

Basis—Day count basis0(实际/实际)(default) |integer from0to13

Principal—Notional principal amounts or principal value schedules100(default) |vector or cell array

EndMonthRule—End-of-month rule flag for generating dates whenMaturityis end-of-month date for month having 30 or fewer days1(in effect)(default) |nonnegative integer[0,1]

AdjustCashFlowsBasis—Flag to adjust cash flows based on actual period day countfalse(default) |value of0(false) or1(true)

Holidays—Holidays used in computing business daysif not specified, the default is to useholidays.m(default) |MATLAB®date numbers

BusinessDayConvention—Business day conventionsactual(default) |特征向量|cell array of character vectors

CapRate—Annual cap ratedecimal

FloorRate—Annual floor ratedecimal

Output Arguments

Price预期的浮动利率0时刻注意价格vector

PriceTree— Tree structure of instrument pricesstructure

More About

Floating-Rate Note

References

See Also

Topics

Financial Instruments Toolbox Documentation

金宝app

A Practical Guide to Modeling Financial Risk with MATLAB

`CIRTree`—Interest-rate tree structure
structure

`Spread`—Number of basis points over the reference rate
vector

`Settle`—Settlement date
serial date number|特征向量|string array|datetime

`Maturity`—Maturity date
serial date number|特征向量|string array|datetime

`FloatReset`—Frequency of payments per year
`1`(default) |vector

`Basis`—Day count basis
`0`(实际/实际)(default) |integer from`0`to`13`

`Principal`—Notional principal amounts or principal value schedules
`100`(default) |vector or cell array

`EndMonthRule`—End-of-month rule flag for generating dates when`Maturity`is end-of-month date for month having 30 or fewer days
`1`(in effect)(default) |nonnegative integer`[0,1]`

`AdjustCashFlowsBasis`—Flag to adjust cash flows based on actual period day count
`false`(default) |value of`0`(false) or`1`(true)

`Holidays`—Holidays used in computing business days
if not specified, the default is to use`holidays.m`(default) |MATLAB^®date numbers

`BusinessDayConvention`—Business day conventions
`actual`(default) |特征向量|cell array of character vectors

`CapRate`—Annual cap rate
decimal

`FloorRate`—Annual floor rate
decimal

`Price`预期的浮动利率0时刻注意价格
vector

`PriceTree`— Tree structure of instrument prices
structure