bdttree

Build Black-Derman-Toy interest-rate tree

Syntax

BDTTree = bdttree(VolSpec,RateSpec,TimeSpec)

Description

BDTTree = bdttree(VolSpec,RateSpec,TimeSpec) creates a structure containing time and interest-rate information on a recombining tree.

Note

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

Examples

Create a BDTTree

Using the data provided, create a BDT volatility specification (using bdtvolspec), rate specification (using intenvset), and tree time layout specification (using bdttimespec). Then use these specifications to create a BDT tree with bdttree.

Compounding = 1;
ValuationDate = '01-01-2000';
StartDate = ValuationDate;
EndDates = ['01-01-2001'; '01-01-2002'; '01-01-2003'; 
'01-01-2004'; '01-01-2005'];
Rates = [.1; .11; .12; .125; .13];
Volatility = [.2; .19; .18; .17; .16];

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

Use treeviewer to observe the tree you have created.

treeviewer(BDTTree)

Input Arguments

VolSpec — Volatility process specification

structure

Volatility process specification, specified using the VolSpec output obtained from bdtvolspec.

Data Types: struct

RateSpec — Interest-rate specification for initial risk-free rate curve

structure

Interest-rate specification for initial rate curve, specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

TimeSpec — Time tree layout specification

structure

Time tree layout specification, specified using the TimeSpec output obtained from bdttimespec. The TimeSpec defines the observation dates of the BDT tree and the Compounding rule for date to time mapping and price-yield formulas.

Data Types: struct

Output Arguments

BDTTree — Time and interest-rate information of a recombining tree

structure

Time and interest-rate information of a recombining tree, returned as a structure.

More About

Black-Derman-Toy Interest-Rate Tree

The Black-Derman-Toy (BDT) interest-rate tree is used to represent the evolution of interest rates over time, particularly for pricing interest-rate derivatives.

The BDT interest-rate tree captures the dynamics of interest rates using a binomial tree structure. The BDT interest-rate tree incorporates the concept of a stochastic short rate, which allows for a more realistic representation of interest-rate movements. The BDT model is based on the short rate, which is the instantaneous interest rate at a given time. The BDT model assumes that the short rate follows a lognormal distribution, which ensures that the rates remain positive.

Version History

Introduced before R2006a