Pricing an At-the-Money FX Option from Spot, Volatility, and Rates

Summary

The answer explains how to identify inputs for a European at-the-money currency option using spot FX, implied volatility, and deposit rates. For an option on a currency forward, it first derives the forward level from spot and the interest-rate differential under covered interest rate parity. Because the option is at the money, the strike is set equal to that forward level. The USD deposit rate is then used as the discount rate in the Black–Scholes calculation described by the answer.

For an option on currency spot instead, the response says to use the quoted spot exchange rate as the underlying price, without first calculating a forward. The example assumes continuously compounded deposit rates and parity holds exactly, as stipulated in the question. It is a brief setup explanation rather than a full derivation or numerical option valuation, and does not address conventions such as quote currency, notional, or whether the option’s ATM definition is forward or spot based beyond the stated case.

Key ideas

• For a currency-forward underlying, covered interest rate parity converts spot into a forward price.
• An at-the-money strike is set equal to the relevant underlying level in the example.
• The answer uses the USD deposit rate as the discount rate for the option calculation.
• For a currency-spot underlying, the quoted spot rate is used directly.
• The explanation assumes continuous compounding and exact covered interest rate parity.

Tags

# Computing option price with rates only


# Computing option price with rates only












Hi I am learning about options and came across this example:

The spot FX rate AUD/USD is 0.6868, 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.

I would like to compute the price of this European put option. But from the given information I dont see what is spot price, strike price and risk free interest rate. Could you please help me?

## Answer by Dhruv Mahajan (score 1, accepted)

https://quant.stackexchange.com/a/46286

Please recheck, from what i can understand this question is trying to test pricing for currency options on currency forwards.Spot price is $0.6868$. If underlying is a currency forward, the underlying price $S0$ would be the forward price calculated using the interest rate parity. $$ S0 = 0.6868*\exp((0.028 - 0.0145)*0.5) $$ ATM options means strike price is also $S0$.

Risk free rate is the USD deposit rate = $0.028$

Now you can use the BS formula to calculate the option price.

If the option is on currency spot, no need to calculate the forward price, simply use $0.6868$

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