Pricing Currency Options with Domestic and Foreign Interest Rates

Summary

The document explains how to represent foreign and domestic interest rates when pricing an option on a currency pair. In its AUD/USD example, the question is whether the Australian deposit rate acts like a dividend yield and whether the pricing function should use both rates. The answer says the foreign rate is equivalent to a dividend yield in this framework, while the US rate is used as the discount rate.

For the cited binomial option function, the cost of carry is the domestic rate minus the foreign rate, and the discounting rate is the domestic rate. This captures the effect of holding the foreign currency while valuing the option in the domestic currency. The response is concise and does not walk through the tree calculations or provide a numerical option price; its parameter mapping depends on the function’s conventions and the currency quote orientation.

Key ideas

• The foreign currency deposit rate plays a role analogous to a dividend yield.
• For AUD/USD valued in USD, the domestic rate is the USD rate and the foreign rate is the AUD rate.
• The function’s cost of carry is the domestic rate minus the foreign rate.
• The domestic rate is used for discounting in the described binomial setup.

Tags

# Domestic and foreign interest rate; dividends?


# Domestic and foreign interest rate; dividends?












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)
```

## Answer by Magic is in the chain (score 2, accepted)

https://quant.stackexchange.com/a/46314

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