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The spot price AUD/USD is 0.6868, strike price is 0.6915,the 6 month ATM implied volatility for AUD/USD is 7.7% p.a., for the 6 month USD deposit rate is 2.28% and the 6 month AUD deposit rate is 1.45% p.a. Deposits are continuously compounded and the covered interest rate parity works perfectly. Underlying asset is a currency forward or currency spot. Compute the price of European put option.

My question is: is the rate for the AUD deposit (foreign rate) actually a dividend rate? If not, is it okay to only use USD deposit rate in binomial model(code below).If it is a dividend rate, how can I add dividends to this function? I tried to solve my problem reading this,but it didnt help much.

library('fOptions')
CRRBinomialTreeOption(TypeFlag ="pe", S, X,
Time, r, b, sigma, n, title = NULL, description = NULL)
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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 $r_{USD}$.

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