bdttrans (Financial Toolbox)

bdttrans
Translate a tree returned by bdtbond

Syntax

bdttrans(Tree)
[TreeMat, TreeTimes] = bdttrans(Tree)

Arguments

Tree
Tree structure returned by bdtbond.

`Tree`	Tree structure returned by `bdtbond`.

Description
bdttrans unpacks and converts a short discount tree structure to a short rate tree, or a price tree structure to a clean price tree. The output is a matrix of tree node values and a vector of node times.

TreeMat is an NSTATES-by-NTIMES converted matrix of short rate or clean price values at points on the tree. Time layers are columns containing the different states. Unused entries of the matrix are screened with NaN.

TreeTimes is a 1-by-NTIMES vector of times corresponding to layers of TreeMat.

If bdttrans is called without output arguments, it plots the translated tree against the time axis in coupon intervals.

Examples
Specify a bond.

OptBond.Settle = '15-Jul-1996';
OptBond.Maturity = '15-Jan-1998';
OptBond.CouponRate = 0.07;
OptBond.Period = 2;

Specify an embedded American call option. Make the bond callable by the issuer between 15-Jan-1997 and maturity.

OptBond.CallType = 1;
OptBond.CallStartDate = '15-Jan-1997';
OptBond.CallExpiryDate = '15-Jan-1998';
OptBond.CallStrike = 101;

Build constant zero curve structure.

ZeroCurve.ZeroRates = 0.05; 
ZeroCurve.CurveDates = '15-Jul-1996';

Build constant volatility curve structure.

VolCurve.VolatilityRates = 0.15; 
VolCurve.CurveDates = '15-Jul-1996';

Choose two tree nodes per whole coupon period.

Accuracy = 2;

Run the bdtbond function.

[Price, Sensitivities, DiscTree, PriceTree] = bdtbond(OptBond,...       
ZeroCurve, VolCurve, Accuracy);

Convert the discount tree to a short rate tree.

DiscTree = 
Values: [6x7 double]
Times: [0 0.5000 1 1.5000 2 2.5000 3]
Dates: [729221 729313 729405 729496 729586 729678 729770]
ErrorFlag: 0
Type: 'Short Discount'
Frequency: 2

[ShortRateMat, TreeTimes] = bdttrans(DiscTree)

ShortRateMat =

0.0500   0.0500   0.0447   0.0399   0.0357   0.0319   0.0285
   NaN      NaN   0.0554   0.0494   0.0442   0.0395   0.0353
   NaN      NaN      NaN   0.0613   0.0548   0.0489   0.0437
   NaN      NaN      NaN      NaN   0.0679   0.0607   0.0542
   NaN      NaN      NaN      NaN      NaN   0.0753   0.0672
   NaN      NaN      NaN      NaN      NaN      NaN   0.0835

TreeTimes =

0    0.5000    1.0000    1.5000    2.0000    2.5000    3.0000

Convert the price tree to a clean price tree.

PriceTree = 
Values: [6x7 double]
Times: [0 0.5000 1 1.5000 2 2.5000 3]
Dates: [729221 729313 729405 729496 729586 729678 729770]
ErrorFlag: 0
AccrInt: [0 1.7500 0 1.7597 0 1.7500 0]
Coupons: [0 0 3.5000 0 3.5000 0 3.5000]
Type: 'Price'

[CleanPriceMat, TreeTimes] = bdttrans(PriceTree)

CleanPriceMat =

101.9512  101.4677  101.0000  101.0000  101.0000  100.9348  100.0000
     NaN       NaN  101.0000  101.0000  101.0000  100.7429  100.0000
     NaN       NaN       NaN  100.6019  100.7397  100.5060  100.0000
     NaN       NaN       NaN       NaN  100.0978  100.2139  100.0000
     NaN       NaN       NaN       NaN       NaN   99.8539  100.0000
     NaN       NaN       NaN       NaN       NaN       NaN  100.0000

TreeTimes =

0    0.5000    1.0000    1.5000    2.0000    2.5000    3.0000

See Also
bdtbond

bdtbond beytbill