Price double one-touch and double no-touch binary options using Black-Scholes option pricing model
Price a Double No-Touch Option
Compute the price of a double no-touch option using the following data:
AssetPrice = 105; Rate = 0.1; Volatility = 0.2; Settle = '01-Jan-2018'; Maturity = '01-Jul-2018';
RateSpec = intenvset('ValuationDate', Settle, 'StartDates', Settle, 'EndDates', ... Maturity, 'Rates', Rate, 'Compounding', -1);
DividendType = "Continuous"; DividendYield = Rate - 0.03; StockSpec = stockspec(Volatility, AssetPrice, DividendType, DividendYield);
Calculate the price of a double no-touch binary option.
BarrierSpec = "DNT"; Barrier = [120 80]; Payoff = 10; Price = dbltouchbybls(RateSpec, StockSpec, Settle, Maturity, BarrierSpec, Barrier, Payoff)
Price = 5.6368
StockSpec — Stock specification for underlying asset
Stock specification for the underlying asset, specified by the
StockSpec obtained from
stockspec handles several
types of underlying assets. For example, for physical commodities, the price
StockSpec.Asset, the volatility is
StockSpec.Sigma, and the convenience yield is
Settle — Settlement or trade date
serial date number | date character vector | datetime object
Settlement or trade date for the double touch option, specified as an
1 matrix using serial
date numbers, date character vectors, or datetime objects.
Maturity — Maturity date
serial date number | date character vector
Maturity date for the double touch option, specified as an
1 vector of serial date
numbers or date character vectors.
BarrierSpec — Double barrier option type
cell array of character vectors with values of
'DNT' | string array with values of
Double barrier option type, specified as an
1 cell array of character
vectors or string array with the following values:
'DOT'— Double one-touch. The double one-touch option defines two
Barrierlevels. A double one-touch option provides a
Payoffif the underlying asset ever touches either the upper or lower
'DNT'— Double no-touch. The double no-touch option defines two
Barrierlevels. A double no-touch option provides a
Payoffif the underlying asset ever never touches either the upper or lower
Barrier — Double barrier value
Double barrier value, specified as an
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).
Payoff — Payoff value
Payoff value, specified as an
1 matrix of numeric
values, where each element is a
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).
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
BarrierSpec, the payoff is at the
Maturity of the option.
Price — Expected prices for double one-touch options
Expected prices for double one-touch options at time 0, returned as an
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
 Haug, E. The Complete Guide to Option Pricing Formulas. McGraw-Hill Education, 2007.
 Wystup, U. FX Options and Structured Products. Wiley Finance, 2007.