Implied Correlation Skew in Three-Currency FX Options

Summary

The document asks how EUR/JPY option skew relates to the skews of USD/EUR and USD/JPY options. It gives the standard variance relationship for a currency cross: the cross variance depends on the two component variances and their correlation. Rearranging this relationship across strikes yields an implied correlation for each point on the skew.

The observation is that this implied correlation varies across strikes, prompting a request for an intuitive explanation. The document does not provide an answer, supporting data, or a model that explains the variation. It therefore serves as a focused question about how dependence between currency pairs, skew, and option pricing interact; the variance identity alone does not establish why the implied correlation is skewed.

Key ideas

• Cross-currency variance depends on the component variances and their correlation.
• Applying the variance relationship across option strikes can produce strike-dependent implied correlations.
• The document raises, but does not resolve, the question of why implied correlation varies along the skew.

Tags

# 3 pairs, FX options, implied vols


# 3 pairs, FX options, implied vols












I am trying to undertand the relationship between EUR/JPY options and USD/EUR and USD/JPY options. Vol(USD/EUR) = $S_1$, Vol(Usd/JPY) = $S_2$, Vol(EUR/JPY) = $S_3$ The actual Vol follows: \begin{align} S_3^2 = S_1^2 + S_2^2 - 2 \rho(S_1,S_2) S_1 S_2 \end{align}

where $\rho$ is the implied correlation. But looking at the skew of EUR/JPY and trying the above formula, there are differences along the skew, i.e. different correlation or "implied correlation". Question is, can someone explain intuitively why the implied correlation is skewed?

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