hjmtree

Build Heath-Jarrow-Morton interest-rate tree

Syntax

HJMTree = hjmtree(VolSpec,RateSpec,TimeSpec)

Description

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

Examples

Create a HJMTree

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: {1x5 cell}

Use treeviewer to observe the tree you have created.

treeviewer(HJMTree)

Input Arguments

VolSpec — Volatility process specification

structure

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

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 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

HJMTree — Time and interest-rate information of a bushy tree

structure

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