impvbyrgw
Determine implied volatility using Roll-Geske-Whaley option pricing model for American call option
Syntax
Description
computes implied volatility using Roll-Geske-Whaley option pricing model for American call
option.Volatility
= impvbyrgw(RateSpec
,StockSpec
,Settle
,Maturity
,Strike
,OptPrice
)
Note
impvbyrgw
computes implied volatility of
American calls with a single cash dividend using the Roll-Geske-Whaley
option pricing model.
adds
optional name-value pair arguments.Volatility
= impvbyrgw(___,Name,Value
)
Examples
Compute the Implied Volatility Using the Roll-Geske-Whaley Option Pricing Model
This example shows how to compute the implied volatility using the Roll-Geske-Whaley option pricing model. Assume that on July 1, 2008 a stock is trading at $13 and pays a single cash dividend of $0.25 on November 1, 2008. The American call option with a strike price of $15 expires on July 1, 2009 and is trading at $1.346. The annualized continuously compounded risk-free rate is 5% per annum. Calculate the implied volatility of the stock using the Roll-Geske-Whaley option pricing model.
AssetPrice = 13; Strike = 15; Rates = 0.05; Settle = datetime(2008,7,1); Maturity = datetime(2009,7,1); % define the RateSpec and StockSpec RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', -1); StockSpec = stockspec(NaN, AssetPrice, {'cash'}, 0.25, {'Nov 1,2008'}); Price = [1.346]; Volatility = impvbyrgw(RateSpec, StockSpec, Settle, Maturity, Strike, Price)
Volatility = 0.3539
Input Arguments
StockSpec
— Stock specification for underlying asset
structure
Stock specification for the underlying asset. For information
on the stock specification, see stockspec
.
stockspec
handles several
types of underlying assets. For example, for physical commodities
the price is StockSpec.Asset
, the volatility is StockSpec.Sigma
,
and the convenience yield is StockSpec.DividendAmounts
.
Data Types: struct
Settle
— Settlement date
datetime array | string array | date character vector
Settlement date, specified as a NINST
-by-1
vector using
a datetime array, string array, or date character vectors.
To support existing code, impvbyrgw
also
accepts serial date numbers as inputs, but they are not recommended.
Maturity
— Maturity date
datetime array | string array | date character vector
Maturity date for the American option, specified as a
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, impvbyrgw
also
accepts serial date numbers as inputs, but they are not recommended.
Strike
— Option strike price value
nonnegative scalar | nonnegative vector
Option strike price value, specified as a nonnegative scalar
or NINST
-by-1
vector of strike
price values. Each row is the schedule for one option.
Data Types: double
OptPrice
— American option price
nonnegative scalar | nonnegative vector
American option prices from which the implied volatility of
the underlying asset is derived, specified as a nonnegative scalar
or NINST
-by-1
vector.
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: Volatility = impvbyrgw(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,OptPrice,'Limit',5,'Tolerance',1e-5)
Limit
— Upper bound of implied volatility search interval
10
(1000% per annum) (default) | positive value
Upper bound of implied volatility search interval, specified as the comma-separated pair
consisting of 'Limit'
and a positive scalar.
Data Types: double
Tolerance
— Implied volatility search termination tolerance
1e-6
(default) | positive scalar
Implied volatility search termination tolerance, specified as the comma-separated pair
consisting of 'Tolerance'
and a positive
scalar.
Data Types: double
Output Arguments
Volatility
— Expected implied volatility values
vector
Expected implied volatility values, returned as a NINST
-by-1
vector.
If no solution can be found, a NaN
is returned.
Version History
Introduced in R2008bR2022b: Serial date numbers not recommended
Although impvbyrgw
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.
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