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How Vega, Skew, and Curvature Shape FX Volatility Spreads

Article Quant Q&A · Author: Ussu
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Summary

The document explains a proposed ordering of bid–offer spreads for three common foreign exchange volatility structures: at-the-money (ATM), risk reversal (RR), and butterfly (BF). It links the spread width to the exposure market makers must manage, rather than to liquidity alone. In the explanation, an ATM position carries substantial vega exposure; an RR offsets much of its outright volatility exposure and mainly expresses skew; a BF offsets more vega and skew exposure and mainly expresses curvature.

On that basis, the answer argues that market makers may demand the widest spread for ATM, a narrower one for RR, and the narrowest for BF as the dominant risks become more contained. This is a risk-based rationale, not a universal empirical law or a quantified comparison. Actual quotes can also depend on liquidity and market conditions, and the document provides no data to measure those influences or test the stated ordering.

Key ideas

  • The explanation attributes ATM spreads to substantial vega risk.
  • A risk reversal offsets much of its outright volatility exposure and mainly reflects skew exposure.
  • A butterfly is described as having limited vega and skew exposure, with curvature as its main risk.
  • The proposed spread ordering follows market makers' risk compensation, but no empirical evidence is provided.

Tags

ForexOptionsVolatilityMarket microstructureDerivatives pricing
Full text
# Relation between ATM, RR and BF


# Relation between ATM, RR and BF












In FX derivative market, why does vol spread of ATM > RR > BF? ATM is the most liquid and intuitively it should have the lowest spread. Please help me in understanding the rational behind the above logic.

## Answer by Chris Taylor (score 8)

https://quant.stackexchange.com/a/49078

The ATM is an outright position (long 50 delta put and 50 delta call) so the main exposure is vega. It is the riskiest of the three, and demands a higher bid-offer spread from market makers to compensate them for the additional risk.

The RR is a spread position (long 25 delta call, short 25 delta put) with little vega, the main exposure is skew. Because the outright risk is hedged, market makers are willing to quote a tighter bid-offer spread.

The BF is a spread of spreads (long 25 delta call vs short 50 delta call, and long 25 delta put vs short 50 delta put) so it has little exposure to vega or skew. The main exposure is curvature. Hence it carries even lower risk than the ATM and RR, so market makers are willing to quote the lowest bid-offer spread.

Shown in full with attribution under the source's licence. Licence: CC BY-SA 4.0 (Stack Exchange)

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