gapbybls
Determine price of gap digital options using Black-Scholes model
Description
Examples
Compute Gap Option Prices Using the Black-Scholes Option Pricing Model
This example shows how to compute gap option prices using the Black-Scholes option pricing model. Consider a gap call and put options on a nondividend paying stock with a strike of 57 and expiring on January 1, 2008. On July 1, 2008 the stock is trading at 50. Using this data, compute the price of the option if the risk-free rate is 9%, the strike threshold is 50, and the volatility is 20%.
Settle = datetime(2008,1,1); Maturity = datetime(2008,7,1); Compounding = -1; Rates = 0.09; % calculate the RateSpec RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle,... 'EndDates', Maturity, 'Rates', Rates, 'Compounding', Compounding, 'Basis', 1); % define the StockSpec AssetPrice = 50; Sigma = .2; StockSpec = stockspec(Sigma, AssetPrice); % define the call and put options OptSpec = {'call'; 'put'}; Strike = 57; StrikeThreshold = 50; % calculate the price Pgap = gapbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec,... Strike, StrikeThreshold)
Pgap = 2×1
-0.0053
4.4866
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, gapbybls
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, gapbybls
also
accepts serial date numbers as inputs, but they are not recommended.
OptSpec
— Definition of option
character vector with values 'call'
or
'put'
| cell array of character vectors with values 'call'
or
'put'
Definition of the option as 'call'
or
'put'
, specified as an
NINST
-by-1
vector.
Data Types: char
| cell
Strike
— Pay-off strike value
vector
Pay-off strike value, specified as an
NINST
-by-1
vector.
Data Types: double
StrikeThreshold
— Strike values that determine if the option pays off
vector
Strike values that determine if the option pays off, specified as an
NINST
-by-1
vector.
Data Types: double
Output Arguments
Price
— Expected prices for gap option
vector
Expected prices for gap option, returned as a
NINST
-by-1
vector.
More About
Gap Option
A gap option is a digital option in which one strike decides if the option is in or out of money and another strike decides the size the size of the payoff.
Version History
Introduced in R2009aR2022b: Serial date numbers not recommended
Although gapbybls
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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