supersharebybls
Determine price of supershare digital options using Black-Scholes model
Description
Examples
Compute the Price of Supershare Digital Options Using Black-Scholes Model
This example shows how to compute the price of supershare digital options using Black-Scholes model. Consider a supershare based on a portfolio of nondividend paying stocks with a lower strike of 350 and an upper strike of 450. The value of the portfolio on November 1, 2008 is 400. The risk-free rate is 4.5% and the volatility is 18%. Using this data, calculate the price of the supershare option on February 1, 2009.
Settle = datetime(2008,11,1); Maturity = datetime(2009,2,1); Rates = 0.045; Basis = 1; Compounding = -1; % create the RateSpec RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', Basis); % define the StockSpec AssetPrice = 400; Sigma = .18; StockSpec = stockspec(Sigma, AssetPrice); % define the high and low strike points StrikeLow = 350; StrikeHigh = 450; % calculate the price Pssh = supersharebybls(RateSpec, StockSpec, Settle, Maturity,... StrikeLow, StrikeHigh)
Pssh = 0.9411
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 or trade date
datetime array | string array | date character vector
Settlement or trade date for the basket option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, supersharebybls
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 basket option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, supersharebybls
also
accepts serial date numbers as inputs, but they are not recommended.
StrikeLow
— Low strike price values
vector
Low strike price values, specified as an
NINST
-by-1
vector.
Data Types: double
StrikeHigh
— High strike price values
vector
High strike price values, specified as an
NINST
-by-1
vector.
Data Types: double
Output Arguments
Price
— Expected prices for supershare option
vector
Expected prices for supershare option, returned as a
NINST
-by-1
vector.
More About
Supershare Option
A supershare option pays out a proportion of the assets underlying a portfolio if the asset lies between a lower and an upper bound at the expiry of the option.
For more information, see Digital Option.
Version History
Introduced in R2009aR2022b: Serial date numbers not recommended
Although supersharebybls
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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