touchsensbybls

Calculate price or sensitivities for one-touch and no-touch binary options using Black-Scholes option pricing model

Syntax

PriceSens = touchsensbybls(RateSpec,StockSpec,Settle,Maturity,BarrierSpec,Barrier,Payoff)

PriceSens = touchsensbybls(___,Name,Value)

Description

PriceSens = touchsensbybls(RateSpec,StockSpec,Settle,Maturity,BarrierSpec,Barrier,Payoff) calculates the price and sensitivities for one-touch and no-touch binary options using the Black-Scholes option pricing model.

PriceSens = touchsensbybls(___,Name,Value) specifies options using one or more name-value pair arguments in addition to the input arguments in the previous syntax.

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 = '01-Jan-2018';
Maturity = '01-Jul-2018';

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 = 9.7264

Delta = -0.8939

Gamma = 0.0616

Input Arguments

RateSpec — Interest-rate term structure

structure

Interest-rate term structure (annualized and continuously compounded), specified by the RateSpec obtained from intenvset. For information on the interest-rate specification, see intenvset.

Data Types: struct

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

serial date number | date character vector | datetime object

Settlement or trade date for the touch option, specified as an NINST-by-1 matrix using serial date numbers, date character vectors, or datetime objects.

Data Types: double | char | datetime

Maturity — Maturity date

serial date number | date character vector

Maturity date for the touch option, specified as an NINST-by-1 vector of serial date numbers or date character vectors.

Data Types: double | char | cell

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 the Barrier level and the payoff is zero otherwise.

• 'NT' — No-touch. The no-touch option provides a Payoff if the underlying spot ever never trades at or beyond the Barrier level and the Payoff 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 Pair Arguments

Specify optional comma-separated pairs of Name,Value arguments. Name is the argument name and Value is the corresponding value. Name must appear inside quotes. You can specify several name and value pair arguments in any order as Name1,Value1,...,NameN,ValueN.

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.