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Build Heath-Jarrow-Morton interest-rate tree



HJMTree = hjmtree(VolSpec,RateSpec,TimeSpec) creates a structure containing time and forward-rate information on a bushy tree.


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Using the data provided, create a HJM volatility specification (using hjmvolspec), rate specification (using intenvset), and tree time layout specification (using hjmtimespec). Then use these specifications to create a HJM tree using hjmtree.

Compounding = 1;
ValuationDate = '01-01-2000';
StartDate = ['01-01-2000'; '01-01-2001'; '01-01-2002'; '01-01-2003'; '01-01-2004'];
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];
CurveTerm = [1; 2; 3; 4; 5]; 

HJMVolSpec = hjmvolspec('Stationary', Volatility , CurveTerm);

RateSpec = intenvset('Compounding', Compounding,...
                     'ValuationDate', ValuationDate,...
                     'StartDates', StartDate,...
                     'EndDates', EndDates,...
                     'Rates', Rates);

HJMTimeSpec = hjmtimespec(ValuationDate, EndDates, Compounding);
HJMTree = hjmtree(HJMVolSpec, RateSpec, HJMTimeSpec)
HJMTree = struct with fields:
      FinObj: 'HJMFwdTree'
     VolSpec: [1x1 struct]
    TimeSpec: [1x1 struct]
    RateSpec: [1x1 struct]
        tObs: [0 1 2 3 4]
        dObs: [730486 730852 731217 731582 731947]
        TFwd: {[5x1 double]  [4x1 double]  [3x1 double]  [2x1 double]  [4]}
      CFlowT: {[5x1 double]  [4x1 double]  [3x1 double]  [2x1 double]  [5]}
     FwdTree: {[5x1 double]  [4x1x2 double]  [3x2x2 double]  [2x4x2 double]  [1x8x2 double]}

Use treeviewer to observe the tree you have created.


Input Arguments

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Volatility process specification, specified using the VolSpec output obtained from hjmvolspec. VolSpec sets the number of factors and the rules for computing the volatility σ(t,T) for each factor.

Data Types: struct

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

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

Data Types: struct

Output Arguments

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

Version History

Introduced before R2006a