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Price floor instrument from Hull-White interest-rate tree



[Price,PriceTree] = floorbyhw(HWTree,Strike,Settle,Maturity) computes the price of a floor instrument from a Hull-White interest-rate tree. capbyhw computes prices of vanilla floors and amortizing floors.


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] = floorbyhw(___,FloorReset,Basis,Principal,Options) adds optional arguments.


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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 = datetime(2004,1,1);
Maturity = datetime(2007,1,1);

Use floorbyhw to compute the price of the floor instrument.

Price = floorbyhw(HWTree, Strike, Settle, Maturity)
Price = 0.4186

Define the RateSpec.

Rates = [0.035; 0.042; 0.047; 0.052; 0.054];
ValuationDate = datetime(2014,4,1);
StartDates = ValuationDate;
EndDates = datetime(2019,4,1);
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 = datetime(2014,4,1);
Maturity = datetime(2018,4,1);
Strike = 0.05;
FloorReset = 1;
Principal ={{datetime(2015,4,1) 100;datetime(2016,4,1) 60;datetime(2017,4,1) 40;datetime(2018,4,1) 20};

Build the HW Tree.

VolDates = [datetime(2015,4,1) ; datetime(2016,4,1) ; datetime(2017,4,1) ; datetime(2018,4,1)];
VolCurve = 0.05;
AlphaDates = datetime(2018,4,1);
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: {[1.0350]  [1.1300 1.0363 0.9503]  [1.2363 1.1337 1.0397 0.9534 0.8743]  [1.3544 1.2421 1.1390 1.0445 0.9579 0.8784 0.8056]}

Price the amortizing and vanilla floors.

Basis = 0;
Price  = floorbyhw(HWTree, Strike, Settle, Maturity, FloorReset, Basis, Principal)
Price = 2×1


Input Arguments

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Interest-rate tree structure, specified by using hwtree.

Data Types: struct

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

Data Types: double

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 HW tree. The floor argument Settle is ignored.

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

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, floorbyhw also accepts serial date numbers as inputs, but they are not recommended.

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

Data Types: double

(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

(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

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

Data Types: struct

Output Arguments

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

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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

Introduced before R2006a

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