When the payoff from an FX derivatives contract is based on more than one currency pair it is described as a multi-asset option. Having multiple currency pairs within an option structure adds extra dimensions and can significantly increase risk management complexity.
Standard Greek exposures are not sufficient for managing multi-asset risk. Single values for delta, gamma, and vega make little sense when the exposures in a given currency pair depend not just on changes in that currency pair but on all the currency pairs within the structure.
It is therefore vital for a trader to understand the methodology used to calculate exposures on multi-asset products within their pricing and risk management systems. If standard Greek exposures are used to risk manage multi-asset options, they certainly rely on strict assumptions about how the underlying assets move together. This can lead to big risk management shocks when the assumptions break down.
Correlations between spot log returns are key parameters within the multi-asset framework. When pricing the two-currency-pair case, for intuition it is often useful to consider how the option payoff is impacted by perfectly positively correlated spots, perfectly negatively correlated spots, and spots with zero correlation. For multi-asset options with more than two currency pairs, correlations are often viewed within a matrix. For example, the following three-asset correlation matrix ...