Gets the delta for different options, Vanilla and Foreign for all contract types
It is tricky to decide what form to use. Should the delta be with respect to 1/$S, or with respect to $S? For the binary bets, whether foreign or domestic we are differentiating with respect to $S.
For a vanilla, the correct way should be with respect to 1/$S (so that we know how many units of the domestic currency to hedge), but to keep things standard, we do it with respect to $S.
For example take USDJPY vanilla call with premium in USD. Thus this is a vanilla contract on JPY. Thus delta with respect to 1/$S tells us how many units of JPY to hedge, but with respect to $S, there really isn't a meaning and needs to be converted back before interpretation.