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Interpreting Volatility Skew and the Limits of a Short Butterfly

Article Quant Q&A · Author: Victor
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Summary

The discussion considers whether higher implied volatility for out-of-the-money calls and puts points to a particular options spread. It describes this pattern as a volatility smile and reasons within a Black–Scholes comparison: because option vega is generally positive, options quoted with higher implied volatility appear more expensive than at-the-money options quoted with lower implied volatility. On that relative-value view, the proposed position is to sell the wings and buy options near at-the-money, approximated by a short butterfly.

The answer stresses that this is not a ready-made real-market strategy. The apparent mispricing depends on using a Black–Scholes framework that does not capture the volatility shape observed in markets, and the spread’s payoff does not by itself establish that the options are mispriced. The discussion gives no market data, hedge rules, expiry selection, or performance evidence; a trader would need a suitable volatility model and risk assessment before implementation.

Key ideas

  • Higher implied volatility in the wings indicates higher option prices within a Black–Scholes comparison.
  • The suggested relative-value position sells wing options and buys options nearer at-the-money.
  • A short butterfly is offered as an approximation to that position.
  • Observed volatility skew alone does not prove a tradable mispricing or establish profitability.
  • Real-world implementation requires a framework that accounts for market volatility shapes and risk.

Tags

OptionsVolatilityDerivatives pricingRisk management
Full text
# Strategy for implied volatility


# Strategy for implied volatility












I encountered this question: "A trader observed that the implied vol of OTM calls and puts are higher than that of ATM option, what is the best strategy among: Calendar Spread, Bull Spread, Bear Spread and Butterfly ?"

Is this a trick question? For me, what the trader observed is simply the standard volatility smile shape, which for foreign currency options is given below:

Only if other traders didn't knew this volatility shape and were using the regular Black-Scholes pricing model, could the trader capitalize on this discovery. Then, the calls with high strike price would be under-priced and the puts with low strike price would be also under-priced. The trader then would want to buy lots of calls with high strike price and lots of puts with low strike price. Besides, none of the payoffs above take advantage of this property. (Maybe shorting a butterfly spread?)

## Answer by AdB (score 3)

https://quant.stackexchange.com/a/44886

Firstly, remember that in general vega is positive for all options. Hence, the fact that the implied volatility is higher in the wings (high and low strikes, i.e. deep ITM/OTM) means that these options are over-priced. Thus, you would want to sell/short these options. By the same logic, you would want to buy/long options around the ATM point where implied volatility is low. Therefore, you would want to short the butterfly spread (since you believe realized volatility will increase in the future).

As you mention, it is correct that this mispricing is compared to a Black-Scholes framework. We know that in reality, the assumptions in B-S are not consistent with what we expect to see in the actual markets. Hence, if you want to implement a vol strategy in real life, you cannot simply use the above strategy.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.