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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?

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  • $\begingroup$ Is the underlying asset of the option a stock, futures on a currency pair, etc, or anything else about its life span like whether it can be exercised early (American vs European)? also which price are you looking for, call price or put price $\endgroup$ – develarist Jun 25 at 10:52
  • $\begingroup$ @develarist I edited question and added information $\endgroup$ – Maria Jun 25 at 11:00
  • $\begingroup$ Are you sure it is on a stock? I think the option is on a currency forward or currency spot. If it is so, the question is easy. $\endgroup$ – Dhruv Mahajan Jun 25 at 13:03
  • $\begingroup$ @Dhruv Mahajan would you then be so kind and post the answer if it is one of those? $\endgroup$ – Maria Jun 25 at 13:07
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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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  • $\begingroup$ Thanks. So if the option is on currency spot, S0=spot price=strike price? $\endgroup$ – Maria Jun 25 at 13:27
  • $\begingroup$ Yes because the option is ATM $\endgroup$ – Dhruv Mahajan Jun 25 at 13:28
  • $\begingroup$ And USD deposit rate is domestic rate? $\endgroup$ – Maria Jun 25 at 13:29
  • $\begingroup$ Yes because from the currency convention , it is usually given in FC/DC. So if your domestic market is US, US risk free rate should be used. $\endgroup$ – Dhruv Mahajan Jun 25 at 13:31

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