Original paper
Abstract
We extensively study the term structure of volatility in individual equity options. We begin by studying the behavior of implied volatility in the cross section. We examine the joint dynamics of short maturity and long maturity implied volatility in order to gain a thorough understanding of how volatility term structure evolves. We uncover a number of stylized facts which, to the best of our knowledge, we are the first to empirically document. We then propose a simple framework of term structure dynamics that captures the features documented in our empirical study. This simple framework is illustrative and gives an intuitive way to understand the dynamics of the volatility term structure seen in the cross section. Using the intuition gleaned from our analysis, we examine strategies for trading volatility. Consistent with the term structure dynamics, we uncover a number of profitable volatility trading strategies across maturities. We further examine the extent to which profitability of these trading strategies is due to an interaction between volatility term structure and realized volatility.
Keywords:Â Equity Options, Term Structure, Volatility
Trading rules
- Consider all options within the U.S. equity market for investment.
- Construct straddles on the day after the standard monthly options expiration, which is every third Friday of the month.
- Exclude:
- Options that don't meet arbitrage standards,
- Those related to stocks priced below 10 USD,
- Non-ATM options with a delta not within 0.35 (-0.35) and 0.65 (-0.65) for calls (puts).
- Focus on options with maturities between one and six months.
- Organize the portfolio considering the gradient of the implied volatility term structure.
- Categorize into deciles:
- The first decile represents the most positive slope in the term structure.
- The tenth decile has the steepest negative slope.
- Strategy: Buy decile 1, sell decile 10 of one-month ATM straddles.
- Holding period: Until expiration (one month).
- Portfolio weighting: Equally weighted.
- Investment allocation: 20% of total portfolio value due to leptokurtic skewness.
Python code
Backtrader
import backtrader as bt
import pandas as pd
import numpy as np
from datetime import timedelta
class StraddleStrategy(bt.Strategy):
def __init__(self):
# Custom indicators and calculations for slope and deciles will be required
pass
def next(self):
# Check if today is the day after the third Friday of the month
if (self.datetime.date(0).day > 21) and (self.datetime.date(0) - timedelta(days=1)).weekday() == 4:
# Filter options and calculate slopes, deciles, etc.
# This will require custom data processing and indicators
# Create equal weights for selected options
weights = 1.0 / len(selected_options)
# Enter positions for selected options
for option in selected_options:
self.order_target_percent(data=option, target=weights * 0.2) # 20% of total portfolio value
# Exit positions at expiration (one month holding period)
for option in self.getpositions():
if self.datetime.date(0) >= option.expiration_date:
self.sell(data=option)
if __name__ == '__main__':
cerebro = bt.Cerebro()
cerebro.addstrategy(StraddleStrategy)
# Add U.S. equity options data feed here
cerebro.run()This code provides a basic framework for the StraddleStrategy. You will need to implement the custom data processing and indicators to filter options based on the given rules, calculate the slopes of implied volatility term structures, and assign deciles. Additionally, you will need to provide a custom data feed containing the necessary U.S. equity options data.