bktree

Build Black-Karasinski interest-rate tree

Syntax

BKTree = bktree(VolSpec,RateSpec,TimeSpec)

BKTree = bktree(___,Name,Value)

Description

BKTree = bktree(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.

BKTree = bktree(___,Name,Value) adds additional name-value pair arguments.

Examples

Create a BKTree

Using the data provided, create a BK volatility specification (using bkvolspec), rate specification (using intenvset), and tree time layout specification (using bktimespec). Then use these specifications to create a BK tree using bktree.

Compounding = -1;
ValuationDate = '01-01-2004';
StartDate = ValuationDate;
VolDates = ['12-31-2004'; '12-31-2005'; '12-31-2006'; 
'12-31-2007'];
VolCurve = 0.01;
AlphaDates = '01-01-2008';
AlphaCurve = 0.1;
Rates = [0.0275; 0.0312; 0.0363; 0.0415];

BKVolSpec = bkvolspec(ValuationDate, VolDates, VolCurve,...  
AlphaDates, AlphaCurve);

RateSpec = intenvset('Compounding', Compounding,...
		     'ValuationDate', ValuationDate,...
		     'StartDates', ValuationDate,...
		     'EndDates', VolDates,...
		     'Rates', Rates);
 
BKTimeSpec = bktimespec(ValuationDate, VolDates, Compounding);

BKTree = bktree(BKVolSpec, RateSpec, BKTimeSpec)

BKTree = struct with fields:
      FinObj: 'BKFwdTree'
     VolSpec: [1×1 struct]
    TimeSpec: [1×1 struct]
    RateSpec: [1×1 struct]
        tObs: [0 0.9973 1.9973 2.9973]
        dObs: [731947 732312 732677 733042]
      CFlowT: {[4×1 double]  [3×1 double]  [2×1 double]  [3.9973]}
       Probs: {[3×1 double]  [3×3 double]  [3×5 double]}
     Connect: {[2]  [2 3 4]  [2 3 4 5 6]}
     FwdTree: {[1.0278]  [1.0361 1.0355 1.0349]  [1.0493 1.0484 1.0476 1.0467 1.0459]  [1.0620 1.0609 1.0598 1.0587 1.0577 1.0567 1.0557]}

Use treeviewer to observe the tree you have created.

treeviewer(BKTree)

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 BK tree and the Compounding rule for date to time mapping and price-yield formulas.

Data Types: struct

Name-Value Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: BKTree = bktree(BKVolSpec, RateSpec, BKTimeSpec,'Method','HW1996')

Method — Hull-White method upon which the tree-node connectivity algorithm is based

'HW2000' (default) | character vector with values 'HW2000' or 'HW1996'

Hull-White method upon which the tree-node connectivity algorithm is based, specified as a character vector with a value of 'HW2000' or 'HW1996'.

bktree supports two tree-node connectivity algorithms. HW1996 is based on the original paper published in the Journal of Derivatives, and HW2000 is the general version of the algorithm, as specified in the paper published in August 2000.

Data Types: char

Output Arguments

BKTree — 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-Karasinski Interest-Rate Tree

The Black-Karasinski (BK) interest-rate tree is used for the valuation of interest-rate derivatives, particularly in the context of modeling short-term interest rates.

The BK model, which is an extension of the traditional Black-Scholes framework, is adapted to capture the dynamics of interest rates using a stochastic process. The BK interest-rate tree is a discrete-time representation of the continuous-time model.

References

[1] Hull, J., and A. White. "Using Hull-White Interest Rate Trees." Journal of Derivatives. 1996.

[2] Hull, J., and A. White. "The General Hull-White Model and Super Calibration." August 2000.

Version History

Introduced before R2006a