A butterfly option position is an advanced trading strategy that requires a combination of calls and/or puts with three different strike prices of the same maturity. It’s a non-directional options trading strategy that is commonly used when an investor believes that the underlying asset’s price will remain relatively stable in the near future. It can also be used when the trader wants to take advantage of a volatility increase or decrease, depending on which type of butterfly strategy is being employed.
The advantages of using butterfly positions include greater flexibility, as well as the ability to reduce risk exposures. Additionally, it allows traders to take advantage of market conditions without having to predict where the price of the underlying asset will move. For example, if a trader believes that volatility is about to increase, they can use a butterfly option combination to take advantage of the potential increase in volatility.
Reference  proposed a novel trading scheme based on butterflies’ premium.
For each S&P 500 stock, we calculate the rolling correlation between the Cboe Volatility Index (VIX) and the prices of butterfly options at different strikes. The butterfly that co-moves most positively with the VIX reveals the expectation of the stock’s return in a future market crash and is called the butterfly implied return (BIR). A long-short strategy based on BIR hedges the market downturn while earning an annualized alpha of 3.4% to 4.7%.
We find that this paper offers a fresh perspective on volatility trading. Usually, in a relative-value volatility arbitrage strategy, implied volatilities are used to assess the rich/cheapness of options positions. Here the authors utilized directly the option positions premium to evaluate their relative values.
Let us know what you think in the comments below or in the discussion forum.
 Wu, Di and Yang, Lihai, Butterfly Implied Returns (October 5, 2022). https://ssrn.com/abstract=3880815
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