dbltouchsensbybls
Calculate prices and sensitivities for double one-touch and double no-touch binary options using Black-Scholes option pricing model
Syntax
Description
calculates prices and sensitivities for double one-touch and double no-touch binary
options using the Black-Scholes option pricing model.PriceSens
= dbltouchsensbybls(RateSpec
,StockSpec
,Settle
,Maturity
,BarrierSpec
,Barrier
,Payoff
)
Note
Alternatively, you can use the DoubleTouch
object to calculate price or sensitivities for
double touch options. For more information, see Get Started with Workflows Using Object-Based Framework for Pricing Financial Instruments.
specifies options using one or more name-value pair arguments in addition to the
input arguments in the previous syntax.PriceSens
= dbltouchsensbybls(___,Name,Value
)
Examples
Calculate the Price and Sensitivities for a Double No-Touch Option
Compute the price and sensitivities for a double no-touch option using the following data:
AssetPrice = 105; Rate = 0.1; Volatility = 0.2; Settle = datetime(2018,1,1); Maturity = datetime(2018,6,1);
Define the RateSpec
using intenvset
.
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', ... Maturity, 'Rates', Rate, 'Compounding', -1);
Define the StockSpec
using stockspec
.
DividendType = "Continuous";
DividendYield = Rate - 0.03;
StockSpec = stockspec(Volatility, AssetPrice, DividendType, DividendYield);
Define the sensitivities.
OutSpec = {'price', 'delta', 'gamma'};
Calculate the price and sensitivities for a double no-touch binary option.
BarrierSpec = "DNT"; Barrier = [120 80]; Payoff = 10; [Price, Delta, Gamma] = dbltouchsensbybls(RateSpec, StockSpec, Settle, Maturity, BarrierSpec, Barrier, Payoff,'OutSpec',OutSpec)
Price = 6.3082
Delta = -0.2770
Gamma = -0.0311
Input Arguments
StockSpec
— Stock specification for underlying asset
structure
Stock specification for the underlying asset, specified by the
StockSpec
obtained from 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 double touch option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, dbltouchsensbybls
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 double touch option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, dbltouchsensbybls
also
accepts serial date numbers as inputs, but they are not recommended.
BarrierSpec
— Double barrier option type
cell array of character vectors with values of 'DOT'
or 'DNT'
| string array with values of "DOT"
or
"DNT"
Double barrier option type, specified as an
NINST
-by-1
cell array of character
vectors or string array with the following values:
'DOT'
— Double one-touch. The double one-touch option defines twoBarrier
levels. A double one-touch option provides aPayoff
if the underlying asset ever touches either the upper or lowerBarrier
levels.'DNT'
— Double no-touch. The double no-touch option defines twoBarrier
levels. A double no-touch option provides aPayoff
if the underlying asset ever never touches either the upper or lowerBarrier
levels.
Data Types: char
| cell
| string
Barrier
— Double barrier value
numeric
Double barrier value, specified as an
NINST
-by-2
matrix of numeric
values, where the first column is Upper Barrier(1)(UB) and the second column
is Lower Barrier(2)(LB). Barrier(1) must be greater than Barrier(2).
Data Types: double
Payoff
— Payoff value
numeric
Payoff value, specified as an
NINST
-by-1
matrix of numeric
values, where each element is a 1
-by-2
vector in which the first column is Barrier(1)(UB) and the second column is
Barrier(2)(LB). Barrier(1) must be greater than Barrier(2).
Note
The payoff value is calculated for the point in time that the
Barrier
value is reached. The payoff is
either cash or nothing. If you specify a double no-touch option
using BarrierSpec
, the payoff is at the
Maturity
of the option.
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: PriceSens =
dbltouchsensbybls(RateSpec,StockSpec,OptSpec,Strike,Settle,Maturity,BarrierSpec,Barrier,'OutSpec','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'
| string array with values "Price"
,
"Delta"
, "Gamma"
,
"Vega"
, "Lambda"
,
"Rho"
, "Theta"
, and
"All"
Define outputs, specified as the comma-separated pair consisting of
'OutSpec'
and an 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 double one-touch options
matrix
Expected prices at time 0 or sensitivities (defined using
OutSpec
) for double one-touch options, returned as
an NINST
-by-1
matrix.
More About
Double One-Touch and Double No-Touch Options
Double one-touch options and double no-touch options work the same way as one-touch options, except that there are two barriers.
A double one-touch or double no-touch option provides a payoff if the underlying
spot either ever or never touches either the upper or lower
Barrier
levels. If neither barrier level is breached prior
to expiration, the option expires worthless and the trader loses all the premium
paid to the broker for setting up the trade. For example, if the current USD/EUR
rate is 1.15, and the trader believes that this rate will change significantly over
the next 15 days, the trader can use a double one-touch option with barriers at 1.10
and 1.20. The trader can profit if the rate moves beyond either of the two
barriers.
References
[1] Haug, E. The Complete Guide to Option Pricing Formulas. McGraw-Hill Education, 2007.
[2] Wystup, U. FX Options and Structured Products. Wiley Finance, 2007.
Version History
Introduced in R2019bR2022b: Serial date numbers not recommended
Although dbltouchsensbybls
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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