Risk Reversals, Log-Strike Symmetry, and Volatility Smile Effects

Summary

The document raises questions about how volatility smiles affect the strikes used to construct currency risk reversals. It asks why, under a flat smile, strikes are approximately symmetric around at-the-money in log space, and why that symmetry can place the topside strike farther from at-the-money in ordinary spot terms. It also asks how implied volatility at a fixed delta changes the strike needed to reach that delta.

The text suggests that higher implied volatility moves a fixed-delta strike farther from at-the-money, while lower volatility moves it closer. It also proposes that short-dated risk reversals mainly reflect expected spot moves and realized volatility, whereas longer-dated ones are more affected by implied volatility changes. These points are posed for explanation rather than demonstrated: the document gives no derivation, pricing model, data, or evidence to establish them. The proposed maturity distinction should therefore be treated as a hypothesis, not a universal rule.

Key ideas

• A flat volatility smile is associated with approximate symmetry of risk-reversal strikes in log space.
• A fixed-delta strike may move farther from or closer to at-the-money as implied volatility changes.
• The document proposes that spot moves and realized volatility matter more at short tenors.
• It proposes a larger role for implied volatility changes in longer-tenor risk reversals.
• The document asks for explanations but does not provide a mathematical derivation or empirical support.

Tags

# Risk reversal basics and trading strategies


# Risk reversal basics and trading strategies












It it written in the book by Giles Jewitt: "If a currency pair had a completely flat volatility smile, the risk reversal strikes would be positioned approximately symmetrically around the ATM strike in logspace. Therefore, the topside strike will be further away from the ATM than the downside strike in regular spot space. At short maturities this effect is small but at longer maturities the impact can be significant." Please explain why strikes are symmetrically distributed in log-space?

Please give mathematical or intuitive rational for the below:

- If the implied volatility for a given delta is higher on the smile, the strike moves further away from the ATM; think about the increasing chance of ending up in-the-money at higher volatility.

- If the implied volatility for a given delta is lower on the smile, the strike moves closer to the ATM; think about the decreasing chance of ending up in-the-money at lower volatility.

- At shorter tenors the risk reversal is largely driven by expectations of spot moves and realized spot volatility.

- At longer tenors the risk reversal is largely driven by expectations of spot moves and implied volatility changes.

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