compoundbycrr

Price compound option from Cox-Ross-Rubinstein binomial tree

Syntax

[Price,PriceTree] = compoundbycrr(CRRTree,UOptSpec,UStrike,USettle,UExerciseDates,UAmericanOpt,COptSpec,CStrike,CSettle,CExerciseDates)

[Price,PriceTree] = compoundbycrr(___,CAmericanOpt)

Description

[Price,PriceTree] = compoundbycrr(CRRTree,UOptSpec,UStrike,USettle,UExerciseDates,UAmericanOpt,COptSpec,CStrike,CSettle,CExerciseDates) prices compound options from a Cox-Ross-Rubinstein binomial tree.

[Price,PriceTree] = compoundbycrr(___,CAmericanOpt) adds an optional argument for CAmericanOpt.

Examples

Price a Compound Option Using a CRR Binomial Tree

This example shows how to price a compound option using a CRR binomial tree by loading the file deriv.mat, which provides CRRTree. The CRRTree structure contains the stock specification and time information needed to price the option.

load deriv.mat

UOptSpec = 'Call';
UStrike = 130;
USettle = datetime(2003,1,1);
UExerciseDates = datetime(2006,1,1);
UAmericanOpt = 1;
COptSpec = 'Put';
CStrike = 5;
CSettle = datetime(2003,1,1);
CExerciseDates = datetime(2005,1,1);

Price = compoundbycrr(CRRTree, UOptSpec, UStrike, USettle, ... 
UExerciseDates, UAmericanOpt, COptSpec, CStrike, CSettle, ... 
CExerciseDates)

Price = 
2.8482

Input Arguments

CRRTree — Stock tree structure

structure

Stock tree structure, specified by using crrtree.

Data Types: struct

UOptSpec — Definition of underlying option

character vector with value 'call' or 'put'

Definition of underlying option, specified as 'call' or 'put' using a character vector.

Data Types: char

UStrike — Underlying option strike price value

nonnegative integer

Underlying option strike price value, specified with a nonnegative integer using a 1-by-1 vector.

Data Types: double

USettle — Underlying option settlement date or trade date

datetime array | string array | date character vector

Underlying option settlement date or trade date, specified as a 1-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, compoundbycrr also accepts serial date numbers as inputs, but they are not recommended.

UExerciseDates — Underlying option exercise date

datetime array | string array | date character vector

Underlying option exercise date, specified as a datetime array, string array, or date character vectors:

• For a European option, use a1-by-1 vector of the underlying exercise date. For a European option, there is only one ExerciseDates on the option expiry date.

• For an American option, use a 1-by-2 vector of the underlying exercise date boundaries. The option can be exercised on any tree date. If only one non-NaN date is listed, or if ExerciseDates is 1-by-1, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDates.

To support existing code, compoundbycrr also accepts serial date numbers as inputs, but they are not recommended.

UAmericanOpt — Underlying option type

0 European (default) | scalar with values 0 or 1

Underlying option type, specified as NINST-by-1 positive integer scalar flags with values:

• 0 — European

• 1 — American

If UAmericanOpt is a NaN or is unspecified, the option is a European option.

Data Types: double

COptSpec — Definition of compound option

character vector with value 'call' or 'put' | cell array of character vectors with values 'call' or 'put'

Definition of compound option, specified as 'call' or 'put' using a character vector or a cell array of character vectors with values 'call' or 'put'.

Data Types: char | cell

CStrike — Compound option strike price values

nonnegative integers

Compound option strike price values for a European and American option, specified with a nonnegative integer using a NINST-by-1 matrix. Each row is the schedule for one option.

Data Types: double

CSettle — Compound option settlement date or trade date

datetime array | string array | date character vector

Compound option settlement date or trade date, specified as a 1-by-1 vector using a datetime array, string array, or date character vectors.

To support existing code, compoundbycrr also accepts serial date numbers as inputs, but they are not recommended.

CExerciseDates — Compound option exercise dates

datetime array | string array | date character vector

Compound option exercise dates, specified as a datetime array, string array, or date character vectors:

• For a European option, use aNINST-by-1 matrix of the compound exercise dates. Each row is the schedule for one option. For a European option, there is only one ExerciseDates on the option expiry date.

• For an American option, use a NINST-by-2 vector of the compound exercise date boundaries. For each instrument, the option can be exercised on any tree date between or including the pair of dates on that row. If only one non-NaN date is listed, or if ExerciseDates is NINST-by-1, the option can be exercised between ValuationDate of the stock tree and the single listed ExerciseDates.

To support existing code, compoundbycrr also accepts serial date numbers as inputs, but they are not recommended.

CAmericanOpt — Compound option type

0 European (default) | scalar with values 0 or 1

(Optional) Compound option type, specified as NINST-by-1 positive integer scalar flags with values:

• 0 — European

• 1 — American

If CAmericanOpt is a NaN or is unspecified, the option is a European option.

Data Types: double

Output Arguments

Price — Expected prices for compound options at time 0

vector

Expected prices for compound options at time 0, returned as a NINST-by-1 vector.

PriceTree — Structure with vector of compound option prices at each node

tree structure

Structure with a vector of compound option prices at each node, returned as a tree structure.

PriceTree is a MATLAB^® structure of trees containing vectors of instrument prices and a vector of observation times for each node.

PriceTree.PTree contains the prices.

PriceTree.tObs contains the observation times.

PriceTree.dObs contains the observation dates.

More About

Compound Option

A compound option is basically an option on an option; it gives the holder the right to buy or sell another option.

With a compound option, a vanilla stock option serves as the underlying instrument. Compound options thus have two strike prices and two exercise dates. For more information, see Compound Option.

References

[1] Rubinstein, Mark. “Double Trouble.” Risk. Vol. 5, 1991, p. 73.

Version History

Introduced before R2006a

R2022b: Serial date numbers not recommended

Although compoundbycrr supports serial date numbers, datetime values are recommended instead. The datetime data type provides flexible date and time formats, storage out to nanosecond precision, and properties to account for time zones and daylight saving time.

To convert serial date numbers or text to datetime values, use the datetime function. For example:

t = datetime(738427.656845093,"ConvertFrom","datenum");
y = year(t)

y =

        2021

There are no plans to remove support for serial date number inputs.