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Price swaption from Black-Derman-Toy interest-rate tree


[Price,PriceTree] = swaptionbybdt(BDTTree,OptSpec,Strike,ExerciseDates,Spread,Settle,Maturity)
[Price,PriceTree] = swaptionbybdt(___Name,Value)



[Price,PriceTree] = swaptionbybdt(BDTTree,OptSpec,Strike,ExerciseDates,Spread,Settle,Maturity) prices swaption using a Black-Derman-Toy tree.


[Price,PriceTree] = swaptionbybdt(___Name,Value) adds optional name-value pair arguments.


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This example shows how to price a 5-year call swaption using a BDT interest-rate tree. Assume that interest rate and volatility are fixed at 6% and 20% annually between the valuation date of the tree until its maturity. Build a tree with the following data.

Rates = 0.06 * ones (10,1);      
StartDates = ['jan-1-2007';'jan-1-2008';'jan-1-2009';'jan-1-2010';'jan-1-2011';...

EndDates =['jan-1-2008';'jan-1-2009';'jan-1-2010';'jan-1-2011';'jan-1-2012';...
ValuationDate = 'jan-1-2007'; 
Compounding = 1; 

% define the RateSpec
RateSpec = intenvset('Rates', Rates, 'StartDates', StartDates, 'EndDates', EndDates, ...
'Compounding', Compounding);

% use VolSpec to compute interest-rate volatility
Volatility = 0.20 * ones (10,1);  VolSpec = bdtvolspec(ValuationDate,...
EndDates, Volatility);

% use TimeSpec to specify the structure of the time layout for a BDT tree
TimeSpec = bdttimespec(ValuationDate, EndDates, Compounding);

% build the BDT tree
BDTTree = bdttree(VolSpec, RateSpec, TimeSpec); 

% use the following swaption arguments
ExerciseDates = 'jan-1-2012';
SwapSettlement = ExerciseDates;
SwapMaturity   = 'jan-1-2015'; 
Spread = 0;
SwapReset = 1; 
Principal = 100;
OptSpec = 'call';

% price the swaption
[Price, PriceTree] = swaptionbybdt(BDTTree, OptSpec, Strike, ExerciseDates, ...
Spread, SwapSettlement, SwapMaturity, 'SwapReset', SwapReset, ...
'Basis', Basis, 'Principal', Principal)
Price = 2.0592
PriceTree = struct with fields:
    FinObj: 'BDTPriceTree'
      tObs: [0 1 2 3 4 5 6 7 8 9 10]
     PTree: {[2.0592]  [0.9218 3.4436]  [0.2189 1.7137 5.6694]  [0 0.4549 3.1715 9.1499]  [0 0 0.9524 5.8347 14.3819]  [0 0 0 2.0127 10.6474 21.7783]  [0 0 0 0 0 0 0]  [0 0 0 0 0 0 0 0]  [0 0 0 0 0 0 0 0 0]  [0 0 0 0 0 0 0 0 0 0]  [0 0 0 0 0 0 0 0 0 0]}

Input Arguments

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Interest-rate tree structure, specified by using bdttree.

Data Types: struct

Definition of the option as 'call' or 'put', specified as a NINST-by-1 cell array of character vectors. For more information, see Definitions.

Data Types: char | cell

Strike swap rate values, specified as a NINST-by-1 vector.

Data Types: double

Exercise dates for the swaption, specified as a NINST-by-1 vector or NINST-by-2 using serial date numbers or date character vectors, depending on the option type.

  • For a European option, ExerciseDates are a NINST-by-1 vector of exercise dates. Each row is the schedule for one option. When using a European option, there is only one ExerciseDate on the option expiry date.

  • For an American option, ExerciseDates are a NINST-by-2 vector of exercise date boundaries. For each instrument, the option can be exercised on any coupon date between or including the pair of dates on that row. If only one non-NaN date is listed, or if ExerciseDates is NINST-by-1, the option can be exercised between the ValuationDate of the tree and the single listed ExerciseDate.

Data Types: double | char | cell

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

Data Types: double

Settlement date (representing the settle date for each swap), specified as a NINST-by-1 vector of serial date numbers or a date character vectors. The Settle date for every swaption is set to the ValuationDate of the BDT Tree. The swap argument Settle is ignored. The underlying swap starts at the maturity of the swaption.

Data Types: double | char

Maturity date for each swap, specified as a NINST-by-1 vector of dates using serial date numbers or date character vectors.

Data Types: double | char | cell

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

Example: [Price,PriceTree] = swaptionbybdt(BDTTree,OptSpec, ExerciseDates,Spread,Settle,Maturity,'SwapReset',4,'Basis',5,'Principal',10000)

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(Optional) Option type, specified as NINST-by-1 positive integer flags with values:

  • 0 — European

  • 1 — American

Data Types: double

Reset frequency per year for the underlying swap, specified as a NINST-by-1 vector.

Data Types: double

Day-count basis representing the basis used when annualizing the input forward rate tree for each instrument, 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

Notional principal amount, specified as a NINST-by-1 vector.

Data Types: double

Derivatives pricing options structure, specified using derivset.

Data Types: struct

Output Arguments

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Expected prices of the swaptions 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 swaption instrument prices and a vector of observation times for each node. Within PriceTree:

  • PriceTree.PTree contains the clean prices.

  • PriceTree.tObs contains the observation times.

More About

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Call Swaption

A Call swaption or Payer swaption allows the option buyer to enter into an interest-rate swap in which the buyer of the option pays the fixed rate and receives the floating rate.

Put Swaption

A Put swaption or Receiver swaption allows the option buyer to enter into an interest-rate swap in which the buyer of the option receives the fixed rate and pays the floating rate.

Introduced before R2006a

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