touchsensbybls
Calculate price or sensitivities for one-touch and no-touch binary options using Black-Scholes option pricing model
Syntax
Description
calculates the price and sensitivities for one-touch and no-touch binary options
using the Black-Scholes option pricing model.PriceSens
= touchsensbybls(RateSpec
,StockSpec
,Settle
,Maturity
,BarrierSpec
,Barrier
,Payoff
)
Note
Alternatively, you can use the Touch
object
to calculate price or sensitivities for one 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
= touchsensbybls(___,Name,Value
)
Examples
Calculate the Price and Sensitivities for a One-Touch Option
Compute the price and sensitivities for a one-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 - 0.1;
StockSpec = stockspec(Volatility, AssetPrice, DividendType, DividendYield);
Define the sensitivities.
OutSpec = {'price', 'delta', 'gamma'};
Calculate the price and sensitivities for a one-touch binary option.
BarrierSpec = "OT"; Barrier = 100; Payoff = 15; [Price, Delta, Gamma] = touchsensbybls(RateSpec, StockSpec, Settle, Maturity, BarrierSpec, Barrier, Payoff,'OutSpec',OutSpec)
Price = 9.4102
Delta = -0.9415
Gamma = 0.0685
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 touch option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, touchsensbybls
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 touch option, specified as an
NINST
-by-1
vector using a datetime
array, string array, or date character vectors.
To support existing code, touchsensbybls
also
accepts serial date numbers as inputs, but they are not recommended.
BarrierSpec
— Barrier option type
character vector with values 'OT'
or
'NT'
Barrier option type, specified as an
NINST
-by-1
cell array of character
vectors with the following values:
'OT'
— One-touch. The one-touch option provides a payoff if the underlying spot ever trades at or beyond theBarrier
level and the payoff is zero otherwise.'NT'
— No-touch. The no-touch option provides aPayoff
if the underlying spot ever never trades at or beyond theBarrier
level and thePayoff
is zero otherwise.
Data Types: char
| cell
Barrier
— Barrier value
numeric
Barrier value, specified as an
NINST
-by-1
matrix of numeric
values.
Data Types: double
Payoff
— Payoff value
numeric
Payoff value, specified as an
NINST
-by-1
matrix of numeric values.
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 a no-touch option is specified using the
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: Price =
touchsensbybls(RateSpec,StockSpec,Settle,Maturity,BarrierSpec,Barrier,Payoff,'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'
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 one-touch options
matrix
Expected prices at time 0 or sensitivities (defined using
OutSpec
) for one-touch options, returned as an
NINST
-by-1
matrix.
More About
Touch and No-Touch Options
The one-touch and no-touch options provide a payoff if the underlying spot either ever or never trades at or beyond the barrier level. Otherwise, the payoff is zero.
Only two outcomes are possible with a one-touch option if a trader holds the contract all the way through expiration:
The target price (
Barrier
) is reached and the trader collects the full premium.The target price (
Barrier
) is not reached and the trader loses the amount originally paid to open the trade.
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 touchsensbybls
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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