Vega Risk for Composite-Volatility Commodity Quanto Options

Summary

The document raises a risk-measurement question for quanto-style options on commodity forwards whose payoff is converted through foreign exchange. It gives a composite-volatility formula that combines the underlying commodity volatility, FX volatility, and their correlation. The practical issue is how to report vega: as sensitivity to a change in composite volatility, or as separate sensitivities to the component volatilities. The author also asks whether an ATM-volatility adjustment used for quanto forwards should affect the correlation term.

The author reports that bumping the underlying volatility reproduces Bloomberg OVML results for barrier options, but not for binary, European, or American options away from the strike. This comparison signals a mismatch without identifying its source or supplying a resolved valuation method. The note adds that FX vega can be measured against FX volatility and may be split across the constituent pairs of a cross rate. It leaves the correct convention and platform-specific treatment open, so it is best read as a framing of risk attribution questions rather than a complete pricing guide.

Key ideas

• Composite volatility combines underlying volatility, FX volatility, and their correlation.
• Vega can be expressed against composite volatility or decomposed into sensitivities to component inputs.
• The reported Bloomberg comparison agrees for barriers but not for several other option types away from the strike.
• FX vega may be attributed to FX volatility and divided across the pairs in a cross rate.

Tags

# Compo options on forwards - computing vega correctly


# Compo options on forwards - computing vega correctly












Trying to price compo options on commodity forwards and wondering how vega should be represented.

The vol used to price is the "composite vol", which is: $$\sigma_Y = \sqrt{\sigma_{udl}^2 + \sigma_{FX}^2 + 2\rho_{FX/UDL}\sigma_{udl}\sigma_{FX}}$$

This is fine. The question is what is vega for these products? Do I want to show the risk wrt the composite vol moving or the individual vols moving? Which one does Bloomberg do in OVML?

Bumping the udl and repricing matches OVML (bloomberg) for barriers, but fails for Binary/European/American away from the strike. I feel like this should tell me what is wrong but I haven't managed to fix this.

I know quantos use ATM vol to adjust the forward level, should I be using this in the correl term of the composite vol?

EDIT: FX vega can be computed wrt the FX vol, potentially split by the tradeable pairs in the case of a cross rate.

Thanks!

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