lrtree

Build Leisen-Reimer stock tree

Syntax

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

LRTree = lrtree(___,Name,Value)

Description

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

Note

Alternatively, you can use the AssetTree object to price equity instruments. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.

LRTree = lrtree(___,Name,Value) adds a name-value pair argument.

Examples

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 = struct with fields:
       FinObj: 'BinStockTree'
       Method: 'LR'
    Submethod: 'PP1'
       Strike: 30
    StockSpec: [1×1 struct]
     TimeSpec: [1×1 struct]
     RateSpec: [1×1 struct]
         tObs: [0 0.0041 0.0082 0.0123 0.0164 0.0205 0.0246 0.0288 0.0329 0.0370 0.0411 0.0452 0.0493 0.0534 0.0575 0.0616 0.0657 0.0698 0.0739 0.0780 0.0821 0.0863 0.0904 0.0945 0.0986 0.1027 0.1068 0.1109 0.1150 0.1191 0.1232 0.1273 … ] (1×102 double)
         dObs: [734139 734140 734141 734143 734144 734146 734147 734149 734150 734152 734153 734155 734156 734158 734159 734161 734162 734164 734165 734167 734168 734170 734171 734173 734174 734176 734177 734179 734180 734182 734183 … ] (1×102 double)
        STree: {1×102 cell}
      UpProbs: [101×1 double]

Input Arguments

StockSpec — Stock specification for underlying asset

structure

Stock specification for underlying asset, specified using StockSpec obtained from stockspec. For information on the stock specification, see stockspec.

stockspec can handle other types of underlying assets. For example, stocks, stock indices, and commodities. If dividends are not specified in StockSpec, dividends are assumed to be 0.

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 lrtimespec.

Data Types: struct

Strike — Option strike price value

nonnegative integer

Option strike price value, specified as a scalar nonnegative integer.

Data Types: double

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: LRTree = lrtree(StockSpec,RateSpec,LRTimeSpec,Strike,'Method','PP2')

Method — Computation method

'PP1' (default) | character vector with value 'PP1' or 'PP2'

Computation method, specified as the comma-separated pair consisting of 'Method' and a character vector with a value of 'PP1' or 'PP2'. 'PP1' is for Peizer-Pratt method 1 inversion and 'PP2' is for Peizer-Pratt method 2 inversion. For more information on 'PP1' and 'PP2' methods, see Leisen-Reimer Tree (LR) Modeling.

Data Types: char

Output Arguments

LRTree — Stock and time information for a Leisen-Reimer tree

structure

Stock and time information for a Leisen-Reimer tree, returned as a structure.

More About

Leisen-Reimer Stock Tree

The Leisen-Reimer (LR) stock tree is used for pricing options, particularly in the context of American-style options, which can be exercised at any time before expiration.

The LR stock tree is based on a binomial tree framework that incorporates the potential for early exercise, making it particularly useful for valuing American options.

References

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

Version History

Introduced in R2010b