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As Nap D. Lover said, here you have a list without any dividends being considered. It all depends on your model though. If you are using a stochastic volatility model or similar extensions, you get different Greeks. For the Heston model, for instance, see Chapyer 11 in here. In general however, if you have formulae including a dividend yield $q$, just use ...
Yes it is equivalent of the dividend rate. The b in the function is cost of carry, so here it would be: $b=r_{USD}-r_{AUD}$ And r in the function is $r_{USD}$.