Original paper

SSRN-id1910719.pdf562.8KB

Trading rules

Form a portfolio with a short position in one S&P 500 OTM put option monthly
Strike price distance Z: 1.0x monthly S&P 500 Index standard deviation
Apply constant leverage of 2.0 to the portfolio
Invest unused capital in risk-free rate
Rebalance portfolio and write put options on a monthly basis

Python code

Backtrader

To implement the given trading rules in Backtrader, follow these steps:

Import necessary libraries and modules.
Define the strategy class.
Define the strategy parameters.
Define the __init__ method to initialize the strategy.
Define the next method to execute the strategy logic.
Set up the main script to run the strategy.

Here’s the python code for the strategy:

import backtrader as bt
import mathimport numpy as np

class PutOptionWritingStrategy(bt.Strategy):
    params = (
        ('leverage', 2.0),
        ('strike_price_distance_multiplier', 1.0)
    )

    def __init__(self):
        self.put_option = None
        self.sp500 = self.datas[0]

    def next(self):
        # Calculate the standard deviation of the S&P 500 Index for the last month
        monthly_std = np.std(self.sp500.get(size=21))
        # Calculate the strike price for the put option
        strike_price = self.sp500[0] - (self.params.strike_price_distance_multiplier * monthly_std)
        # Calculate the option premium
        option_premium = max(self.sp500[0] - strike_price, 0)
        # Calculate the required capital to short the put option
        capital_required = option_premium * self.params.leverage
        # Calculate the capital to invest in the risk-free rate
        free_capital = self.broker.get_cash() - capital_required
        # Invest free capital in risk-free rate
        self.buy(data=self.datas[1], size=free_capital)
        # Short the put option
        self.sell(data=self.put_option, size=self.params.leverage, exectype=bt.Order.Put, strike=strike_price)

if __name__ == '__main__':
    cerebro = bt.Cerebro()
    # Add the S&P 500 Index and risk-free rate data feeds
    cerebro.adddata(bt.feeds.YahooFinanceData(dataname='^GSPC', fromdate='2000-01-01', todate='2021-09-30'))
    cerebro.adddata(bt.feeds.FRED(dataname='DTB3', fromdate='2000-01-01', todate='2021-09-30'))
    # Add the put option data feed
    cerebro.adddata(bt.feeds.GenericCSVData(dataname='put_option_data.csv', dtformat=('%Y-%m-%d')))
    cerebro.addstrategy(PutOptionWritingStrategy)
    cerebro.broker.setcash(100000.0)
    cerebro.run()
    cerebro.plot()

Please note that you’ll need to provide a CSV file named ‘put_option_data.csv’ with the put option data. This code assumes that the file has a column named ‘Close’ for the option price and a ‘Date’ column with the format YYYY-MM-DD. Adjust the code as needed based on your data source.

The Cost of Capital for Alternative Investments

Original paper

Trading rules

Python code

Backtrader