Original paper
Abstract
Konstantinidi et. al. state in their broad survey of Volatility-Index forecasting: "The question whether the dynamics of implied volatility indices can be predicted has received little attention". The overall result of this and the quoted papers is: The VIX is too a very limited extend (R2 is typically 0.01) predictable, but the effect is economically not significant.
This paper confirms this finding if (and only if) the forecast horizon is limited to one day. But there is no practical need to do so. One can - and usually does - hold a VIX Future or Option several trading days. It is shown that a simple model has a highly significant predictive power over a longer time horizon. The forecasts improve realistic trading strategies.
Keywords:Â VIX Forecasts, VIX-Options, VIX-Futures
Trading rules
- Engage in trades using VIX futures, and employ the E-mini S&P 500 for hedging.
- When in contango and the daily roll > 0.10 points, sell the nearest VIX futures that still have over 10 business days until maturity.
- When in backwardation and the daily roll < -0.10 points, buy the nearest VIX futures that have more than 10 trading days left to maturity.
- Hold the position for a span of 5 business days and use corresponding E-mini S&P 500 positions to hedge against fluctuations in the spot VIX.
- Calculate daily roll as (front VIX futures price - VIX) / number of business days until settlement.
- Determine hedge ratios using regression analysis of VIX futures price changes and E-mini S&P 500 percentage changes.
Python code
Backtrader
import backtrader as bt
import numpy as np
from sklearn.linear_model import LinearRegression
class VIXFuturesStrategy(bt.Strategy):
def __init__(self):
self.vix = self.datas[0]
self.vix_futures = self.datas[1]
self.es = self.datas[2]
self.order = None
self.hold_days = 0
def next(self):
if self.order:
return
if self.hold_days > 0:
self.hold_days -= 1
return
days_to_maturity = self.vix_futures.days_to_maturity() # Implement this in your data feed
if days_to_maturity < 10:
return
daily_roll = (self.vix_futures[0] - self.vix[0]) / days_to_maturity
if daily_roll > 0.10:
position_size = self.broker.getvalue() * 0.9 / self.vix_futures # Adjust based on your risk management
self.sell(data=self.vix_futures, size=position_size)
hedge_ratio = self.calculate_hedge_ratio()
self.buy(data=self.es, size=position_size * hedge_ratio)
self.hold_days = 5
elif daily_roll < -0.10:
position_size = self.broker.getvalue() * 0.9 / self.vix_futures # Adjust based on your risk management
self.buy(data=self.vix_futures, size=position_size)
hedge_ratio = self.calculate_hedge_ratio()
self.sell(data=self.es, size=position_size * hedge_ratio)
self.hold_days = 5
def calculate_hedge_ratio(self):
vix_futures_returns = np.diff(np.log(self.vix_futures.get(size=252))) # 1-year lookback
es_returns = np.diff(np.log(self.es.get(size=252))) # 1-year lookback
lr = LinearRegression()
lr.fit(es_returns.reshape(-1, 1), vix_futures_returns)
return -lr.coef_[0]
def notify_order(self, order):
if order.status in [order.Submitted, order.Accepted]:
return
if order.status in [order.Completed]:
if order.isbuy():
self.log(f'BUY EXECUTED, {order.executed.price}')
elif order.issell():
self.log(f'SELL EXECUTED, {order.executed.price}')
elif order.status in [order.Canceled, order.Margin, order.Rejected]:
self.log('Order Canceled/Margin/Rejected')
self.order = None