Main Content

floatbycir

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

collapse all in page

Syntax

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

Description

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

floatbycir computes 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.

Note

Alternatively, you can use the FloatBond object to price floating-rate note instruments. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

example

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

example

Examples

collapse all

Open Live Script

Define a Spread of 20-basis points for a floating-rate note.

Spread = 20;

Create a RateSpec using the intenvset function. 

Rates = [0.035; 0.042147; 0.047345; 0.052707]; 
Dates = [datetime(2017,1,1) ; datetime(2018,1,1) ; datetime(2019,1,1) ; datetime(2020,1,1) ; datetime(2021,1,1)]; 
ValuationDate = datetime(2017,1,1); 
EndDates = Dates(2:end)'; 
Compounding = 1; 
RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates', ValuationDate, 'EndDates',EndDates,'Rates', Rates, 'Compounding', Compounding);

Create a CIR tree.

NumPeriods = length(EndDates); 
Alpha = 0.03; 
Theta = 0.02;  
Sigma = 0.1;   
Settle = datetime(2017,1,1); 
Maturity = datetime(2021,1,1); 
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: {[1.0350]  [1.0790 1.0500 1.0298]  [1.1275 1.0887 1.0594 1.0390 1.0270]  [1.1905 1.1406 1.1014 1.0718 1.0512 1.0390 1.0350]}
     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: {[100.7143]  [100.5113 100.5385 100.5589]  [100.3333 100.3508 100.3650 100.3756 100.3821]  [100.1680 100.1753 100.1816 100.1866 100.1903 100.1925 100.1932]  [100 100 100 100 100 100 100]}
     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

          
Interest-rate tree structure, created by cirtree

        
Data Types: struct

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

        
Data Types: double

            
Settlement date, specified either as a scalar or a
              NINST-by-1 vector using a datetime array, string
            array, or date character vectors.

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

            
The Settle date for every floating-rate note is set to the
              ValuationDate of the CIR tree. The floating-rate note argument
              Settle is ignored.

          

            
Maturity date, specified as a NINST-by-1
            vector using a datetime array, string array, or date character vectors representing the
            maturity date for each floating-rate note.

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

          
Name-Value Arguments
Specify optional pairs of arguments as
      Name1=Value1,...,NameN=ValueN, where Name is
      the argument name and Value is the corresponding value.
      Name-value arguments must appear after other arguments, but the order of the
      pairs does not matter.
    

      Before R2021a, use commas to separate each name and value, and enclose 
      Name in quotes.
    
Example: [Price,PriceTree] =
          floatbycir(CIRTree,Spread,Settle,Maturity,'Basis',3)

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

            
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

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


  • 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

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

              
Principal accepts a
                NINST-by-1 vector or
                NINST-by-1 cell array, where each element of
              the cell array is a NumDates-by-2 cell 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

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


  • 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

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

            
Data Types: logical

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

            
Data Types: datetime

              
Business day conventions, specified as the comma-separated pair consisting of
                'BusinessDayConvention' and a character vector or a
                N-by-1 cell 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

              
Annual cap rate, specified as the comma-separated pair consisting of
                'CapRate' and a NINST-by-1
              decimal annual rate or NINST-by-1 cell array,
              where each element is a NumDates-by-2 cell
              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

              
Annual floor rate, specified as the comma-separated pair consisting of
                'FloorRate' and a
                NINST-by-1 decimal annual rate or
                NINST-by-1 cell array. 

            
For the NINST-by-1 cell array, each element
              is a NumDates-by-2 cell 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

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

          

            
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. Within
                PriceTree:


  • PriceTree.PTree contains the clean prices.
  • PriceTree.AITree contains the accrued interest.
  • 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
collapse all
Floating-Rate Note
A floating-rate note is 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.
Version History
Introduced in R2018a
expand all
See Also
 |  |  |  |  |  |  |  |  |  |  |  |  | 
Topics