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Price cash flows from Black-Derman-Toy interest-rate tree



[Price,PriceTree] = cfbybdt(BDTTree,CFlowAmounts,CFlowDates,Settle) prices cash flows from a Black-Derman-Toy interest-rate tree.


[Price,PriceTree] = cfbybdt(___,Basis,Options) adds optional arguments.


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Price a portfolio containing two cash flow instruments paying interest annually over the four-year period from January 1, 2000 to January 1, 2004.

Load the file deriv.mat, which provides BDTTree. The BDTTree structure contains the time and interest-rate information needed to price the instruments.

load deriv.mat;

The valuation date (settle date) specified in BDTTree is January 1, 2000 (date number 730486).

ans = 730486

Provide values for the other required arguments.

CFlowAmounts =[5 NaN 5.5 105; 5 0 6 105];
CFlowDates = [730852, NaN, 731582, 731947; 
              730852, 731217, 731582, 731947];

Use this information to compute the prices of the two cash flow instruments.

[Price, PriceTree] = cfbybdt(BDTTree, CFlowAmounts, ... 
CFlowDates, BDTTree.RateSpec.ValuationDate)
Price = 2×1


PriceTree = struct with fields:
    FinObj: 'BDTPriceTree'
      tObs: [0 1 2 3 4]
     PTree: {[2x1 double]  [2x2 double]  [2x3 double]  [2x4 double]  [2x4 double]}

You can visualize the prices of the two cash flow instruments with the treeviewer function.

Input Arguments

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Interest-rate tree structure, specified by using bdttree.

Data Types: struct

Cash flow amounts, specified as a Number of instruments (NINST) by maximum number of cash flows (MOSTCFS) matrix of cash flow amounts. Each row is a list of cash flow values for one instrument. If an instrument has fewer than MOSTCFS cash flows, the end of the row is padded with NaNs.

Data Types: double

Cash flow dates, specified as NINST-by-MOSTCFS vector using serial date numbers. Each entry contains the date of the corresponding cash flow in CFlowAmounts.

Data Types: double

Settlement date, specified as a vector using serial date numbers or date character vectors. The Settle date for every cash flow is set to the ValuationDate of the BDT tree. The cash flow argument, Settle, is ignored.

Data Types: double | char

(Optional) Day-count basis of the instrument, specified as a 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) Derivatives pricing options structure, specified using derivset.

Data Types: struct

Output Arguments

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Expected 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 observation times for each node. Within PriceTree:

  • PriceTree.PTree contains the clean prices.

  • PriceTree.tObs contains the observation times.

Version History

Introduced before R2006a