lrtree
Build Leisen-Reimer stock tree
Description
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: [1x1 struct]
TimeSpec: [1x1 struct]
RateSpec: [1x1 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 ... ] (1x102 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 ... ] (1x102 double)
STree: {1x102 cell}
UpProbs: [101x1 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
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.
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
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