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Build Leisen-Reimer stock tree


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


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

LRTree = lrtree(StockSpec,RateSpec,TimeSpec,Strike,Name,Value) adds optional name-value pair arguments.

Input Arguments


Stock specification. For more information, see stockspec.


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


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


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.


For Method, use the character vector value 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


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


collapse all

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 = struct with fields:
       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]


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

Introduced in R2010b

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