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hjmprice

Instrument prices from Heath-Jarrow-Morton interest-rate tree

Syntax

Price = hjmprice(HJMTree,InstSet,Options)

Arguments

HJMTree

Heath-Jarrow-Morton tree sampling a forward-rate process. See hjmtree for information on creating HJMTree.

InstSet

Variable containing a collection of instruments. Instruments are categorized by type. Each type can have different data fields. The stored data field is a row vector or character vector for each instrument.

Options

(Optional) Derivatives pricing options structure created with derivset.

Description

Price = hjmprice(HJMTree,InstSet,Options) computes arbitrage-free prices for instruments using an interest-rate tree created with hjmtree. A subset of NINST instruments from a financial instrument variable, InstSet, are priced.

Price is a NINST-by-1 vector of prices for each instrument. The prices are computed by backward dynamic programming on the interest-rate tree. If an instrument cannot be priced, NaN is returned.

PriceTree is a MATLAB® structure of trees containing vectors of instrument prices and accrued interest, and a vector of observation times for each node.

PriceTree.PBush contains the clean prices.

PriceTree.AIBush contains the accrued interest.

PriceTree.tObs contains the observation times.

hjmprice handles instrument types: 'Bond', 'CashFlow', 'OptBond', 'OptEmBond', 'OptEmBond', 'OptFloat', 'OptEmFloat', 'Fixed', 'Float', 'Cap', 'Floor', 'RangeFloat', 'Swap'. See instadd to construct defined types.

Related single-type pricing functions are:

  • bondbyhjm — Price a bond from an HJM tree.

  • capbyhjm — Price a cap from an HJM tree.

  • cfbyhjm — Price an arbitrary set of cash flows from an HJM tree.

  • fixedbyhjm — Price a fixed-rate note from an HJM tree.

  • floatbyhjm — Price a floating-rate note from an HJM tree.

  • floorbyhjm — Price a floor from an HJM tree.

  • optbndbyhjm — Price a bond option from an HJM tree.

  • optembndbyhjm — Price a bond with embedded option by an HJM tree.

  • optfloatbybdt — Price a floating-rate note with an option from an HJM tree.

  • optemfloatbybdt — Price a floating-rate note with an embedded option from an HJM tree.

  • rangefloatbyhjm — Price range floating note using an HJM tree.

  • swapbyhjm — Price a swap from an HJM tree.

  • swaptionbyhjm — Price a swaption from an HJM tree.

Examples

collapse all

Load the HJM tree and instruments from the data file deriv.mat.

load deriv.mat; 
HJMSubSet = instselect(HJMInstSet,'Type', {'Bond', 'Cap'}); 

instdisp(HJMSubSet)
Index Type CouponRate Settle         Maturity       Period Basis EndMonthRule IssueDate FirstCouponDate LastCouponDate StartDate Face Name    Quantity
1     Bond 0.04       01-Jan-2000    01-Jan-2003    1      NaN   NaN          NaN       NaN             NaN            NaN       NaN  4% bond 100     
2     Bond 0.04       01-Jan-2000    01-Jan-2004    2      NaN   NaN          NaN       NaN             NaN            NaN       NaN  4% bond  50     
 
Index Type Strike Settle         Maturity       CapReset Basis Principal Name   Quantity
3     Cap  0.03   01-Jan-2000    01-Jan-2004    1        NaN   NaN       3% Cap 30       

Use hjmprice to price the instruments.

[Price, PriceTree] = hjmprice(HJMTree, HJMSubSet)
Warning: Not all cash flows are aligned with the tree. Result will be approximated. 
> In checktree (line 289)
  In hjmprice (line 85) 

Price =

   98.7159
   97.5280
    6.2831


PriceTree = 

    FinObj: 'HJMPriceTree'
     PBush: {[3x1 double]  [3x1x2 double]  [3x2x2 double]  [3x4x2 double]  [3x8 double]}
    AIBush: {[3x1 double]  [3x1x2 double]  [3x2x2 double]  [3x4x2 double]  [3x8 double]}
      tObs: [0 1 2 3 4]

You can use treeviewer to see the prices of these three instruments along the price tree.

treeviewer

The data for the interest-rate term structure is as follows:

Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = 'Jan-1-2010';
StartDates = ValuationDate;
EndDates = {'Jan-1-2011'; 'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'};
Compounding = 1;

Create a RateSpec.

RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RS = struct with fields:
           FinObj: 'RateSpec'
      Compounding: 1
             Disc: [4x1 double]
            Rates: [4x1 double]
         EndTimes: [4x1 double]
       StartTimes: [4x1 double]
         EndDates: [4x1 double]
       StartDates: 734139
    ValuationDate: 734139
            Basis: 0
     EndMonthRule: 1

Create a portfolio of stepped coupon bonds with different maturities.

Settle = '01-Jan-2010';
Maturity = {'01-Jan-2011';'01-Jan-2012';'01-Jan-2013';'01-Jan-2014'};
CouponRate = {{'01-Jan-2011' .042;'01-Jan-2012' .05; '01-Jan-2013' .06; '01-Jan-2014' .07}};

ISet = instbond(CouponRate, Settle, Maturity, 1);
instdisp(ISet)
Index Type CouponRate Settle         Maturity       Period Basis EndMonthRule IssueDate FirstCouponDate LastCouponDate StartDate Face
1     Bond [Cell]     01-Jan-2010    01-Jan-2011    1      0     1            NaN       NaN             NaN            NaN       100 
2     Bond [Cell]     01-Jan-2010    01-Jan-2012    1      0     1            NaN       NaN             NaN            NaN       100 
3     Bond [Cell]     01-Jan-2010    01-Jan-2013    1      0     1            NaN       NaN             NaN            NaN       100 
4     Bond [Cell]     01-Jan-2010    01-Jan-2014    1      0     1            NaN       NaN             NaN            NaN       100 
 

Build the tree with the following data:

Volatility = [.2; .19; .18; .17];
CurveTerm = [ 1;  2;   3;   4];
HJMTimeSpec = hjmtimespec(ValuationDate, EndDates);
HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6);
HJMT = hjmtree(HJMVolSpec,RS,HJMTimeSpec)
HJMT = struct with fields:
      FinObj: 'HJMFwdTree'
     VolSpec: [1x1 struct]
    TimeSpec: [1x1 struct]
    RateSpec: [1x1 struct]
        tObs: [0 1 2 3]
        dObs: [734139 734504 734869 735235]
        TFwd: {[4x1 double]  [3x1 double]  [2x1 double]  [3]}
      CFlowT: {[4x1 double]  [3x1 double]  [2x1 double]  [4]}
     FwdTree: {[4x1 double]  [3x1x2 double]  [2x2x2 double]  [1x4x2 double]}

Compute the price of the stepped coupon bonds.

PHJM = hjmprice(HJMT, ISet)
PHJM = 

  100.6763
  100.7368
  100.9266
  101.0115

The data for the interest-rate term structure is as follows:

Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = 'Jan-1-2010';
StartDates = ValuationDate;
EndDates = {'Jan-1-2011'; 'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'};
Compounding = 1;

Create a RateSpec.

RS = intenvset('ValuationDate', ValuationDate, 'StartDates', StartDates,...
'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RS = struct with fields:
           FinObj: 'RateSpec'
      Compounding: 1
             Disc: [4x1 double]
            Rates: [4x1 double]
         EndTimes: [4x1 double]
       StartTimes: [4x1 double]
         EndDates: [4x1 double]
       StartDates: 734139
    ValuationDate: 734139
            Basis: 0
     EndMonthRule: 1

Create an instrument portfolio of three stepped callable bonds and three stepped vanilla bonds and display the instrument portfolio.

Settle = '01-Jan-2010';
Maturity = {'01-Jan-2012';'01-Jan-2013';'01-Jan-2014'};
CouponRate = {{'01-Jan-2011' .042;'01-Jan-2012' .05; '01-Jan-2013' .06; '01-Jan-2014' .07}};
OptSpec='call';
Strike=100;
ExerciseDates='01-Jan-2011'; %Callable in one year

% Bonds with embedded option 
ISet = instoptembnd(CouponRate, Settle, Maturity, OptSpec, Strike,...
ExerciseDates, 'Period', 1);
                    
% Vanilla bonds 
ISet = instbond(ISet, CouponRate, Settle, Maturity, 1);

instdisp(ISet)
Index Type      CouponRate Settle         Maturity       OptSpec Strike ExerciseDates  Period Basis EndMonthRule IssueDate FirstCouponDate LastCouponDate StartDate Face AmericanOpt
1     OptEmBond [Cell]     01-Jan-2010    01-Jan-2012    call    100    01-Jan-2011    1      0     1            NaN       NaN             NaN            NaN       100  0          
2     OptEmBond [Cell]     01-Jan-2010    01-Jan-2013    call    100    01-Jan-2011    1      0     1            NaN       NaN             NaN            NaN       100  0          
3     OptEmBond [Cell]     01-Jan-2010    01-Jan-2014    call    100    01-Jan-2011    1      0     1            NaN       NaN             NaN            NaN       100  0          
 
Index Type CouponRate Settle         Maturity       Period Basis EndMonthRule IssueDate FirstCouponDate LastCouponDate StartDate Face
4     Bond [Cell]     01-Jan-2010    01-Jan-2012    1      0     1            NaN       NaN             NaN            NaN       100 
5     Bond [Cell]     01-Jan-2010    01-Jan-2013    1      0     1            NaN       NaN             NaN            NaN       100 
6     Bond [Cell]     01-Jan-2010    01-Jan-2014    1      0     1            NaN       NaN             NaN            NaN       100 
 

Build the tree with the following data:

Volatility = [.2; .19; .18; .17];
CurveTerm = [ 1;  2;   3;   4];
HJMTimeSpec = hjmtimespec(ValuationDate, EndDates);
HJMVolSpec = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6);
HJMT = hjmtree(HJMVolSpec,RS,HJMTimeSpec)
HJMT = struct with fields:
      FinObj: 'HJMFwdTree'
     VolSpec: [1x1 struct]
    TimeSpec: [1x1 struct]
    RateSpec: [1x1 struct]
        tObs: [0 1 2 3]
        dObs: [734139 734504 734869 735235]
        TFwd: {[4x1 double]  [3x1 double]  [2x1 double]  [3]}
      CFlowT: {[4x1 double]  [3x1 double]  [2x1 double]  [4]}
     FwdTree: {[4x1 double]  [3x1x2 double]  [2x2x2 double]  [1x4x2 double]}

Price the instrument set using hjmprice.

PHJM = hjmprice(HJMT, ISet)
PHJM = 

  100.3682
  100.1557
   99.9232
  100.7368
  100.9266
  101.0115

The first three rows correspond to the price of the stepped callable bonds and the last three rows correspond to the price of the stepped vanilla bonds.

The data for the interest-rate term structure is as follows:

Rates = [0.035; 0.042147; 0.047345; 0.052707];
ValuationDate = 'Jan-1-2011';
StartDates = ValuationDate;
EndDates = {'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'; 'Jan-1-2015'};
Compounding = 1;

Create a RateSpec.

RS = intenvset('ValuationDate', ValuationDate, 'StartDates',...
StartDates, 'EndDates', EndDates,'Rates', Rates, 'Compounding', Compounding)
RS = struct with fields:
           FinObj: 'RateSpec'
      Compounding: 1
             Disc: [4x1 double]
            Rates: [4x1 double]
         EndTimes: [4x1 double]
       StartTimes: [4x1 double]
         EndDates: [4x1 double]
       StartDates: 734504
    ValuationDate: 734504
            Basis: 0
     EndMonthRule: 1

Create an instrument portfolio with two range notes and a floating rate note with the following data and display the results:

Spread = 200;
Settle = 'Jan-1-2011';
Maturity = 'Jan-1-2014';

% First Range Note
RateSched(1).Dates = {'Jan-1-2012'; 'Jan-1-2013'  ; 'Jan-1-2014'};
RateSched(1).Rates  = [0.045 0.055; 0.0525  0.0675; 0.06 0.08];

% Second Range Note
RateSched(2).Dates = {'Jan-1-2012'; 'Jan-1-2013' ; 'Jan-1-2014'};
RateSched(2).Rates  = [0.048 0.059; 0.055  0.068 ; 0.07 0.09];

% Create an InstSet
InstSet = instadd('RangeFloat', Spread, Settle, Maturity, RateSched);

% Add a floating-rate note
InstSet = instadd(InstSet, 'Float', Spread, Settle, Maturity);

% Display the portfolio instrument
instdisp(InstSet)
Index Type       Spread Settle         Maturity       RateSched FloatReset Basis Principal EndMonthRule
1     RangeFloat 200    01-Jan-2011    01-Jan-2014    [Struct]  1          0     100       1           
2     RangeFloat 200    01-Jan-2011    01-Jan-2014    [Struct]  1          0     100       1           
 
Index Type  Spread Settle         Maturity       FloatReset Basis Principal EndMonthRule CapRate FloorRate
3     Float 200    01-Jan-2011    01-Jan-2014    1          0     100       1            Inf     -Inf     
 

The data to build the tree is as follows:

Volatility = [.2; .19; .18; .17];
CurveTerm = [ 1;  2;   3;   4];
MaTree = {'Jan-1-2012'; 'Jan-1-2013'; 'Jan-1-2014'; 'Jan-1-2015'};
HJMTS = hjmtimespec(ValuationDate, MaTree);
HJMVS = hjmvolspec('Proportional', Volatility, CurveTerm, 1e6);
HJMT = hjmtree(HJMVS, RS, HJMTS)
HJMT = struct with fields:
      FinObj: 'HJMFwdTree'
     VolSpec: [1x1 struct]
    TimeSpec: [1x1 struct]
    RateSpec: [1x1 struct]
        tObs: [0 1 2 3]
        dObs: [734504 734869 735235 735600]
        TFwd: {[4x1 double]  [3x1 double]  [2x1 double]  [3]}
      CFlowT: {[4x1 double]  [3x1 double]  [2x1 double]  [4]}
     FwdTree: {[4x1 double]  [3x1x2 double]  [2x2x2 double]  [1x4x2 double]}

Price the portfolio.

Price = hjmprice(HJMT, InstSet)
Price = 

   91.1555
   90.6656
  105.5147

Use instswap to create a float-float swap and price the swap with hjmprice.

RateSpec = intenvset('Rates',.05,'StartDate',today,'EndDate',datemnth(today,60));
IS = instswap([.02 .03],today,datemnth(today,60),[], [], [], [1 1]);
VolSpec = hjmvolspec('Constant', .2);
TimeSpec = hjmtimespec(today,cfdates(today,datemnth(today,60),1));
HJMTree = hjmtree(VolSpec,RateSpec,TimeSpec);
hjmprice(HJMTree,IS)
ans = -4.3220

Use instswap to create multiple swaps and price the swaps with hjmprice.

RateSpec = intenvset('Rates',.05,'StartDate',today,'EndDate',datemnth(today,60));
IS = instswap([.03 .02],today,datemnth(today,60),[], [], [], [1 1]);
IS = instswap(IS,[200 300],today,datemnth(today,60),[], [], [], [0 0]);
IS = instswap(IS,[.08 300],today,datemnth(today,60),[], [], [], [1 0]);
VolSpec = hjmvolspec('Constant', .2);
TimeSpec = hjmtimespec(today,cfdates(today,datemnth(today,60),1));
HJMTree = hjmtree(VolSpec,RateSpec,TimeSpec);
hjmprice(HJMTree,IS)
ans = 

    4.3220
   -4.3220
   -0.2701

Introduced before R2006a

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