how would you calculate the fair value of an option on a fx'ed underlying, e.g. a put on a USD-stock which is changed into EUR? How should I get, in practice, the fx spot vol/correl?

Purpose is to have a starting point when dealing with otc structuring desks.



it depends on how it's converted. There are three different possibilities.

  1. the pay-off is $(K-S_T)_+$ with $K$ and $S_T$ in USD but the pay-off is converted to EUR as a predetermined rate. This called a quanto and is widely discussed in books. (eg my book Concepts...)

  2. the pay-off is $(K-S_T)_+$ with $K$ in EUR and $S_T$ in USD. Then you have to model the dynamics of the EUR value of the stock. Which comes down to knowing the FX volatility and the correlation. The first you could get from implied vols of FX options. The second is harder and probably from time series.

  3. the pay-off is $(K-S_T)_+$ with $K$ and $S_T$ in USD but you want to buy it with EUR. In this case, just price in USD and convert with today's exchange rate.


I guess the easiest would be to price a call option, and then use put-call parity. To price the call option you would have to do a change of numeraire. A good reference for this would probably be Brigo and Mercurio.


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