floorbybdt

Price floor instrument from Black-Derman-Toy interest-rate tree

Syntax

[Price,PriceTree] = floorbybdt(BDTTree,Strike,Settle,Maturity)

[Price,PriceTree] = floorbybdt(___,FloorReset,Basis,Principal,Options)

Description

[Price,PriceTree] = floorbybdt(BDTTree,Strike,Settle,Maturity) computes the price of a floor instrument from a Black-Derman-Toy interest-rate tree. floorbybdt computes prices of vanilla floors and amortizing floors.

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

Examples

Price a 10% Floor Instrument Using a BDT Interest-Rate Tree

Load the file deriv.mat, which provides BDTTree. BDTTree 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 = 0.10;
Settle = datetime(2000,1,1);
Maturity = datetime(2004,1,1);

Use floorbybdt to compute the price of the floor instrument.

Price = floorbybdt(BDTTree, Strike, Settle, Maturity)

Price = 
0.2428

Price a 10% Floor Instrument Using a Newly Created BDT Interest-Rate Tree

First set the required arguments for the three needed specifications.

Compounding = 1; 
ValuationDate = datetime(2000,1,1); 
StartDate = ValuationDate; 
EndDates = [datetime(2001,1,1) ; datetime(2002,1,1) ; datetime(2003,1,1) ; datetime(2004,1,1) ;datetime(2005,1,1)]; 
Rates = [.1; .11; .12; .125; .13]; 
Volatility = [.2; .19; .18; .17; .16];

Create the specifications.

RateSpec = intenvset('Compounding', Compounding,... 
'ValuationDate', ValuationDate,... 
'StartDates', StartDate,... 
'EndDates', EndDates,... 
'Rates', Rates); 
BDTTimeSpec = bdttimespec(ValuationDate, EndDates, Compounding); 
BDTVolSpec = bdtvolspec(ValuationDate, EndDates, Volatility);

Create the BDT tree from the specifications.

BDTTree = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec)

BDTTree = struct with fields:
      FinObj: 'BDTFwdTree'
     VolSpec: [1×1 struct]
    TimeSpec: [1×1 struct]
    RateSpec: [1×1 struct]
        tObs: [0 1 2 3 4]
        dObs: [730486 730852 731217 731582 731947]
        TFwd: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [4]}
      CFlowT: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [5]}
     FwdTree: {[1.1000]  [1.0979 1.1432]  [1.0976 1.1377 1.1942]  [1.0872 1.1183 1.1606 1.2179]  [1.0865 1.1134 1.1486 1.1948 1.2552]}

Set the floor arguments. Remaining arguments will use defaults.

FloorStrike = 0.10; 
Settlement = ValuationDate; 
Maturity = datetime(2002,1,1); 
FloorReset = 1;

Use floorbybdt to find the price of the floor instrument.

Price= floorbybdt(BDTTree, FloorStrike, Settlement, Maturity,... 
FloorReset)

Price = 
0.0863

Compute the Price of an Amortizing Floor Using the BDT Model

Define the RateSpec.

Rates = [0.03583; 0.042147; 0.047345; 0.052707; 0.054302];
ValuationDate = datetime(2011,11,15);
StartDates = ValuationDate;
EndDates = [datetime(2012,11,15) ; datetime(2013,11,15) ; datetime(2014,11,15) ; datetime(2015,11,15) ; datetime(2016,11,15)];
Compounding = 1;
RateSpec = intenvset('ValuationDate', ValuationDate,'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)

RateSpec = struct with fields:
           FinObj: 'RateSpec'
      Compounding: 1
             Disc: [5×1 double]
            Rates: [5×1 double]
         EndTimes: [5×1 double]
       StartTimes: [5×1 double]
         EndDates: [5×1 double]
       StartDates: 734822
    ValuationDate: 734822
            Basis: 0
     EndMonthRule: 1

Define the floor instrument.

Settle = datetime(2011,11,15);
Maturity = datetime(2015,11,15);
Strike = 0.039;
Reset = 1;
Principal ={{datetime(2012,11,15) 100;datetime(2013,11,15) 70;datetime(2014,11,15) 40;datetime(2015,11,15) 10}};

Build the BDT Tree.

BDTTimeSpec = bdttimespec(ValuationDate, EndDates);
Volatility = 0.10;  
BDTVolSpec = bdtvolspec(ValuationDate, EndDates, Volatility*ones(1,length(EndDates))');
BDTTree = bdttree(BDTVolSpec, RateSpec, BDTTimeSpec)

BDTTree = struct with fields:
      FinObj: 'BDTFwdTree'
     VolSpec: [1×1 struct]
    TimeSpec: [1×1 struct]
    RateSpec: [1×1 struct]
        tObs: [0 1 2 3 4]
        dObs: [734822 735188 735553 735918 736283]
        TFwd: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [4]}
      CFlowT: {[5×1 double]  [4×1 double]  [3×1 double]  [2×1 double]  [5]}
     FwdTree: {[1.0358]  [1.0437 1.0534]  [1.0469 1.0573 1.0700]  [1.0505 1.0617 1.0754 1.0921]  [1.0401 1.0490 1.0598 1.0731 1.0894]}

Price the amortizing floor.

Basis = 0;
Price = floorbybdt(BDTTree, Strike, Settle, Maturity, Reset, Basis, Principal)

Price = 
0.3060

Input Arguments

BDTTree — Interest-rate tree structure

structure

Interest-rate tree structure, specified by using bdttree.

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

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 BDT tree. The floor argument Settle is ignored.

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

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.

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:

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

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although floorbybdt 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.