gapsensbybls
Determine price or sensitivities of gap digital options using Black-Scholes model
Syntax
Description
specifies options using one or more name-value pair
arguments in addition to the input arguments in the previous
syntax.PriceSens
= gapsensbybls(___,Name,Value
)
Examples
Compute Gap Option Prices and Sensitivities Using the Black-Scholes Option Pricing Model
This example shows how to compute gap option prices and sensitivities 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 and sensitivity 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; %create 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; % compute the price Pgap = gapbybls(RateSpec, StockSpec, Settle, Maturity, OptSpec,... Strike, StrikeThreshold)
Pgap = 2×1
-0.0053
4.4866
% compute the gamma and delta OutSpec = {'gamma'; 'delta'}; [Gamma ,Delta] = gapsensbybls(RateSpec, StockSpec, Settle, Maturity,... OptSpec, Strike, StrikeThreshold, 'OutSpec', OutSpec)
Gamma = 2×1
0.0724
0.0724
Delta = 2×1
0.2852
-0.7148
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, gapsensbybls
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, gapsensbybls
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
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: [Gamma,Delta] =
gapsensbybls(RateSpec,StockSpec,Settle,Maturity,OptSpec,Strike,StrikeThreshold,'OutSpec',{'gamma';
'delta'})
OutSpec
— Define outputs
{'Price'}
(default) | character vector with values
'Price'
,
'Delta'
,
'Gamma'
,
'Vega'
,
'Lambda'
,
'Rho'
,
'Theta'
, and
'All'
| cell array of character vectors with values
'Price'
,
'Delta'
,
'Gamma'
,
'Vega'
,
'Lambda'
,
'Rho'
,
'Theta'
, and
'All'
Define outputs, specified as the
comma-separated pair consisting of
'OutSpec'
and a
NOUT
- by-1
or a
1
-by-NOUT
cell array of character vectors with possible
values of 'Price'
,
'Delta'
,
'Gamma'
,
'Vega'
,
'Lambda'
,
'Rho'
,
'Theta'
, and
'All'
.
OutSpec = {'All'}
specifies that the output is
Delta
,
Gamma
, Vega
,
Lambda
, Rho
,
Theta
, and
Price
, in that order. This is
the same as specifying OutSpec
to include each sensitivity.
Example: OutSpec =
{'delta','gamma','vega','lambda','rho','theta','price'}
Data Types: char
| cell
Output Arguments
PriceSens
— Expected prices or sensitivities for gap option
vector
Expected prices or sensitivities (defined
using OutSpec
) 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 gapsensbybls
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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