lrtree

Build Leisen-Reimer stock tree

Syntax

LRTree = lrtree(StockSpec, RateSpec, TimeSpec, Strike)
LRTree = lrtree(StockSpec, RateSpec, TimeSpec,
Strike, Name,Value)

Description

LRTree = lrtree(StockSpec, RateSpec, TimeSpec, Strike) constructs a Leisen-Reimer stock tree.

LRTree = lrtree(StockSpec, RateSpec, TimeSpec,
Strike, Name,Value)
constructs a Leisen-Reimer stock tree with additional options specified by one or more Name,Value pair arguments.

Input Arguments

StockSpec

Stock specification. For more information, see stockspec.

RateSpec

Interest rate specification of the initial risk-free rate curve. For more information, see intenvset.

TimeSpec

Tree time layout specification. For more information, see lrtimespec.

Strike

Scalar defining the option strike.

Name-Value Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside single quotes (' '). You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

'Method'

String value. Use PP1 for Peizer-Pratt method 1 inversion and PP2 for Peizer-Pratt method 2 inversion. For more information on PP1 and PP2 methods, see Leisen-Reimer Tree (LR) Modeling.

Default: PP1

Output Arguments

LRTree

Structure specifying stock and time information for a Leisen-Reimer tree.

Examples

expand all

Build a Leisen-Reimer Stock Tree

This example shows how to build Leisen-Reimer stock tree. Consider a European put option with an exercise price of $30 that expires on June 1, 2010. The underlying stock is trading at $30 on January 1, 2010 and has a volatility of 30% per annum. The annualized continuously compounded risk-free rate is 5% per annum. Using this data, create a Leisen-Reimer tree with 101 steps using the PP1 method.

AssetPrice = 30;
Strike = 30;

ValuationDate = 'Jan-1-2010';
Maturity = 'June-1-2010';

% define StockSpec
Sigma = 0.3;
StockSpec = stockspec(Sigma, AssetPrice);

% define RateSpec
Rates = 0.05;
Settle = ValuationDate;
Basis = 1;
Compounding = -1;

RateSpec = intenvset('ValuationDate', ValuationDate, 'StartDates', Settle, ...
'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis);

% build the Leisen-Reimer (LR) tree with 101 steps
LRTimeSpec = lrtimespec(ValuationDate, Maturity, 101);

% use the PP1 method
LRMethod  = 'PP1';

LRTree = lrtree(StockSpec, RateSpec, LRTimeSpec, Strike, ...
'method', LRMethod)
LRTree = 

       FinObj: 'BinStockTree'
       Method: 'LR'
    Submethod: 'PP1'
       Strike: 30
    StockSpec: [1x1 struct]
     TimeSpec: [1x1 struct]
     RateSpec: [1x1 struct]
         tObs: [1x102 double]
         dObs: [1x102 double]
        STree: {1x102 cell}
      UpProbs: [101x1 double]

References

Leisen D.P., M. Reimer, "Binomial Models for Option Valuation – Examining and Improving Convergence," Applied Mathematical Finance, Number 3, 1996, pp. 319-346.

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