Barrier Option
Calculate the closed-form price of a single-barrier (knock-in or knock-out, up or down) European option using the Reiner & Rubinstein (1991) formulas.
A barrier option is a path-dependent option whose payoff (and existence) depends on whether the underlying stock price touches a pre-specified barrier level at any point before expiration:
- Knock-out: the option becomes worthless if the barrier is touched.
- Knock-in: the option only comes into existence if the barrier is touched.
- Down barrier: the barrier is below the current stock price.
- Up barrier: the barrier is above the current stock price.
The barrier level is defined relative to the current stock price through barrier_percentage, e.g. a value of 0.9 sets the barrier at 90% of the current stock price (a sensible default for a down barrier).
A useful identity is in-out parity: for identical parameters, a knock-in option plus its corresponding knock-out option (same direction) always equals the price of the equivalent vanilla Black-Scholes option, since the underlying either does or does not touch the barrier.
Also known as: knock-in option, knock-out option, down-and-out, down-and-in, up-and-out, up-and-in option.
Barrier Option in Python
Install the Finance Toolkit with:
pip install financetoolkit -U
Then call get_barrier_option as shown below.
from financetoolkit import Toolkit
toolkit = Toolkit(["AMZN", "AAPL"], api_key="FINANCIAL_MODELING_PREP_KEY")
barrier_option = toolkit.options.get_barrier_option()
barrier_option.loc['AMZN']
Parameters
The function accepts the following parameters:
- start_date (str | None, optional): The start date which determines the stock price. Defaults to None which means it will use the most recent date.
- put_option (bool, optional): Whether to calculate the put option price. Defaults to False which means it will calculate the call option price.
- barrier_percentage (float, optional): The barrier level as a percentage of the current stock price. Defaults to 0.9 which equals 90% of the current stock price.
- barrier_direction (str, optional): Either “down” or “up”. Defaults to “down”.
- knock_type (str, optional): Either “in” or “out”. Defaults to “out”.
- rebate (float, optional): The fixed cash amount paid out if the option knocks out (or fails to knock in). Defaults to 0.0.
- strike_price_range (float): The percentage range to use for the strike prices. Defaults to 0.25 which equals 25% and thus results in strike prices from 75 to 125 if the current stock price is 100.
- strike_step_size (int): The step size to use for the strike prices. Defaults to 5 which means that the strike prices will be 75, 80, 85, 90, 95, 100, 105, 110, 115 and 120 if the current stock price is 100.
- expiration_time_range (int): The number of days to use for the time to expiration. Defaults to 30 which equals 30 days.
- risk_free_rate (float, optional): The risk free rate to use for the calculation. Defaults to None which means it will use the current risk free rate.
- dividend_yield (float, optional): The dividend yield to use for the calculation. Defaults to None which means it will use the dividend yield as obtained through annual historical data.
- show_input_info (bool, optional): Whether to show the input information. Defaults to False.
- rounding (int | None, optional): The number of decimals to round the results to. Defaults to 4.
- standardize (bool, optional): Whether to standardize (Z-Score) the result across the time to expiration columns for each ticker and strike price. Defaults to False.