floorbycir

Price floor instrument from Cox-Ingersoll-Ross interest-rate tree

Syntax

[Price,PriceTree] = floorbycir(CIRTree,Strike,Settle,Maturity)

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

Description

[Price,PriceTree] = floorbycir(CIRTree,Strike,Settle,Maturity) computes the price of a floor instrument from a Cox-Ingersoll-Ross (CIR) interest-rate tree. floorbycir computes prices of vanilla floors and amortizing floors using a CIR++ model with the Nawalka-Beliaeva (NB) approach.

Note

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

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

Examples

Price a Floor Using a CIR Interest-Rate Tree

Define the Strike for a floor.

Strike = 0.02;

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 = 'Jan-1-2017'; 
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 2% floor.

[Price,PriceTree] = floorbycir(CIRT,Strike,Settle,Maturity) 

Price = 
1.4211e-14

PriceTree = struct with fields:
     FinObj: 'CIRPriceTree'
       tObs: [0 1 2 3 4]
      PTree: {[1.4211e-14]  [1.4211e-14 0 -1.4211e-14]  [0 1.4211e-14 0 0 -1.4211e-14]  [0 1.4211e-14 0 0 0 0 0]  [100 100 100 100 100 100 100]}
    Connect: {[3x1 double]  [3x3 double]  [3x5 double]}
      Probs: {[3x1 double]  [3x3 double]  [3x5 double]}

Input Arguments

CIRTree — Interest-rate tree structure

structure

Interest-rate tree structure, specified by using cirtree.

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

datetime array | string array | date character vector

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 CIR tree. The floor argument Settle is ignored.

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

Maturity — Maturity date for floor

datetime array | string array | date character vector

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, floorbycir 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] = floorbycir(CIRTree,CouponRate,Settle,Maturity,'Basis',3)

FloorReset — Reset frequency payment per year

1 (default) | numeric

Reset frequency payment per year, specified as the comma-separated pair consisting of 'FloorReset' and a NINST-by-1 vector.

Data Types: double

Basis — Day-count basis of instrument

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

Day-count basis representing the basis used when annualizing the input forward rate, specified as the comma-separated pair consisting of 'Basis' and 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

Notional principal amount, specified as the comma-separated pair consisting of 'Principal' and a NINST-by-1 of notional principal amounts, or a NINST-by-1 cell array.

For the NINST-by-1 cell array, 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

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:

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

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

R2022b: Serial date numbers not recommended

Although floorbycir supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.