OptionLab

This package is a lightweight library written entirely in Python, designed to provide quick evaluation of option strategies.

The code produces various outputs, including the profit/loss profile of the strategy on a user-defined target date, the range of stock prices for which the strategy is profitable (i.e., generating a return greater than $0.01), the Greeks associated with each leg of the strategy, the resulting debit or credit on the trading account, the maximum and minimum returns within a specified lower and higher price range of the underlying asset, and an estimate of the strategy's probability of profit.

The probability of profit (PoP) for the strategy is calculated based on the distribution of estimated prices of the underlying asset on the user-defined target date. Specifically, for the price range in the payoff where the strategy generates profit, the PoP represents the probability that the stock price will fall within that range. This distribution of underlying asset prices on the target date can be lognormal, log-Laplace, or derived from the Black-Scholes model. Additionally, the distribution can be obtained through simulations (e.g., Monte Carlo) or machine learning models.

Despite the code having been developed with option strategies in mind, it can also be used for strategies that combine options with stocks and/or take into account the profits or losses of closed trades.

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Installation

The easiest way to install OptionLab is using pip:

pip install optionlab

Basic usage

Usage examples for several strategies can be found in Jupyter notebooks in the examples directory.

The evaluation of a strategy is done by calling the run_strategy function provided by the library. This function receives the input data either as a Python dictionary or an Inputs object.

The description of the input data follows:

stock_price : float
- Spot price of the underlying.
volatility : float
- Annualized volatility.
interest_rate : float
- Annualized risk-free interest rate.
min_stock : float
- Minimum value of the stock in the stock price domain.
max_stock : float
- Maximum value of the stock in the stock price domain.
strategy : list
- A list of strategy legs.
dividend_yield : float, optional
- Annualized dividend yield. Default is 0.0.
profit_target : float, optional
- Target profit level. Default is None, which means it is not calculated.
loss_limit : float, optional
- Limit loss level. Default is None, which means it is not calculated.
opt_commission : float
- Broker commission for options transactions. Default is 0.0.
stock_commission : float
- Broker commission for stocks transactions. Default is 0.0.
compute_expectation : logical, optional
- Whether or not the strategy's average profit and loss must be computed from a numpy array of random terminal prices generated from the chosen distribution. Default is False.
discard_nonbusinessdays : logical, optional
- Whether to discard Saturdays and Sundays (and maybe holidays) when counting the number of days between two dates. Default is True.
country : string, optional
- Country for which the holidays will be considered if 'discard_nonbusinessdays' is True. Default is 'US'.
start_date : dt.date, optional
- Start date in the calculations. If not provided, days_to_target_date must be provided.
target_date : dt.date, optional
- Target date in the calculations. If not provided, days_to_target_date must be provided.
days_to_target_date : int, optional
- Number of days until the target date, typically the maturity date of the options. If not provided, start_date and end_date must be provided.
distribution : string, optional
- Statistical distribution used to compute probabilities. It can be 'black-scholes', 'normal', 'laplace' or 'array'. Default is 'black-scholes'.
mc_prices_number : int, optional
- Number of random terminal prices to be generated when calculating the average profit and loss of a strategy. Default is 100,000.

The strategy attribute is a list of strategy legs, where each leg can be of type Option, Stock, or ClosedPosition.

The Option structure:

type : string
- Either 'call' or 'put'. It is mandatory.
strike : float
- Option strike price. It is mandatory.
premium : float
- Option premium. It is mandatory.
n : int
- Number of options. It is mandatory.
action : string
- Either 'buy' or 'sell'. It is mandatory.
prev_pos : float
- Premium effectively paid or received in a previously opened position. If positive, it means that the position remains open and the payoff calculation takes this price into account, not the current price of the option. If negative, it means that the position is closed and the difference between this price and the current price is considered in the payoff calculation.
expiration : string | int
- Expiration date or days to maturity.

Stock:

type : string
- It must be 'stock'. It is mandatory.
n : int
- Number of shares. It is mandatory.
action : string
- Either 'buy' or 'sell'. It is mandatory.
prev_pos : float
- Stock price effectively paid or received in a previously opened position. If positive, it means that the position remains open and the payoff calculation takes this price into account, not the current price of the stock. If negative, it means that the position is closed and the difference between this price and the current price is considered in the payoff calculation.

For a non-determined previously opened position to be closed, which might consist of any combination of calls, puts and stocks, the ClosedPosition must contain two keys:

type : string
- It must be 'closed'. It is mandatory.
prev_pos : float
- The total value of the position to be closed, which can be positive if it made a profit or negative if it is a loss. It is mandatory.

For example, let's say we wanted to calculate the probability of profit for naked calls on Apple stocks with maturity on December 17, 2021. The strategy setup consisted of selling 100 175.00 strike calls for 1.15 each on November 22, 2021.

input_data = {
    "stock_price": 164.04,
    "start_date": "2021-11-22",
    "target_date": "2021-12-17",
    "volatility": 0.272,
    "interest_rate": 0.0002,
    "min_stock": 120,
    "max_stock": 200,
    "strategy": [
        {
            "type": "call",
            "strike": 175.0,
            "premium": 1.15,
            "n": 100,
            "action":"sell"
        }
    ],
}

After defining the input data as a Python dictionary, we pass it to the run_strategy function as shown below:

from optionlab import run_strategy, plot_pl

out = run_strategy(input_data)

plot_pl(out)

The variable out contains an Outputs object with the following structure:

probability_of_profit : float
- Probability of the strategy yielding at least $0.01.
profit_ranges : list
- A list of minimum and maximum stock prices defining ranges in which the strategy makes at least $0.01.
strategy_cost : float
- Total strategy cost.
per_leg_cost : list
- A list of costs, one per strategy leg.
implied_volatility : list
- A Python list of implied volatilities, one per strategy leg.
in_the_money_probability : list
- A list of ITM probabilities, one per strategy leg.
delta : list
- A list of Delta values, one per strategy leg.
gamma : list
- A list of Gamma values, one per strategy leg.
theta : list
- A list of Theta values, one per strategy leg.
vega : list
- A list of Vega values, one per strategy leg.
minimum_return_in_the_domain : float
- Minimum return of the strategy within the stock price domain.
maximum_return_in_the_domain : float
- Maximum return of the strategy within the stock price domain.
probability_of_profit_target : float, optional
- Probability of the strategy yielding at least the profit target.
profit_target_ranges : list, optional
- A list of minimum and maximum stock prices defining ranges in which the strategy makes at least the profit target.
probability_of_loss_limit : float, optional
- Probability of the strategy losing at least the loss limit.
average_profit_from_mc : float, optional
- Average profit as calculated from Monte Carlo-created terminal stock prices for which the strategy is profitable.
average_loss_from_mc : float, optional
- Average loss as calculated from Monte Carlo-created terminal stock prices for which the strategy ends in loss.
probability_of_profit_from_mc : float, optional
- Probability of the strategy yielding at least $0.01 as calculated from Monte Carlo-created terminal stock prices.

To obtain the probability of profit of the naked call example above:

print(f"Probability of Profit (PoP): {(out.probability_of_profit * 100.0):.1f}%%") # 84.5%, according to the calculations

The plot_pl function takes an Outputs object as its argument and plots the profit/loss diagram for the strategy.

Contributions

Dev setup

This repository uses poetry as a package manager. Install poetry as per the poetry docs. It is recommended to install poetry version 1.4.0 if there are issues with the latest versions.

Once poetry is installed, set up your virtual environment for the repository with the following:

cd optionlab/
python3.10 venv venv
source venv/bin/activate
poetry install

That should install all your dependencies and make you ready to contribute. Please add tests for all new features and bug fixes and make sure you are formatting with black.

Optionally, to use Jupyter, you can install it with: pip install juypter.

Git Hooks

This repo uses git hooks. Git hooks are scripts that run automatically every time a particular event occurs in a Git repository. These events can include committing, merging, and pushing, among others. Git hooks allow developers to enforce certain standards or checks before actions are completed in the repository, enhancing the workflow and code quality.

The pre-commit framework is a tool that leverages Git hooks to run checks on the code before it is committed to the repository. By using pre-commit, developers can configure various plugins or hooks that automatically check for syntax errors, formatting issues, or even run tests on the code being committed. This ensures that only code that passes all the defined checks can be added to the repository, helping to maintain code quality and prevent issues from being introduced.

To install the pre-commit framework on a system with Homebrew, follow these steps:

brew install pre-commit

Once pre-commit is installed, navigate to the root directory of your Git repository where you want to enable pre-commit hooks. Then, run the following command to set up pre-commit for that repository. This command installs the Git hook scripts that the pre-commit framework will use to run checks before commits.

pre-commit install

Now, before each commit, the pre-commit hooks you've configured will automatically run. If any hook fails, the commit will be aborted, allowing you to fix the issues before successfully committing your changes. This process helps maintain a high code quality and ensures that common issues are addressed early in the development process.

To check all files in a repository with pre-commit, use:

pre-commit run --all-files

Disclaimer

This is free software and is provided as is. The author makes no guarantee that its results are accurate and is not responsible for any losses caused by the use of the code. Bugs can be reported as issues.