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In a foreign currency model, domestic and foreign stocks + exchange rate is modelled via 3 Wiener processes.

I am trying to price options in this model, however, I am unsure what some realistic values for the volatility vectors are? I am noticing in particular that the value of my price ranges wildly (mainly it goes to 0) for certain volatility choices.

This is because the pricing function contains an exponential to the power of the negative of a dot product of volatility vectors.... so a poor choice of volatilities leads to an incredibly low value due to this exponential factor.

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Using weekly data for the last 5 years for DAX (german equity index), S&P (US equity index) and EUR (value of "german" currency priced in US dollars) we have the following results:

EUR fluctuates with an annualized volatility of 8.8% a year, DAX with vol of 18% a year and S&P vol 12% a year. In my experience it is generally true that a currency is less volatile than a major stock index (as a rough guide about half as volatile). I am a little surprised by how low S&P vol has been, my guess would have been 14 or 15%; DAX typically a little more volatile than S&P and this is confirmed.

The correlations of the currency with the two stock indexes are as follows: EUR with DAX is -0.23. This is in agreement with a general observation I/many people made over the years: when American investors see a foreign stock market go up, they usually see the currency of that country go down and vice versa (not always true of course). Between EUR and S&P correlation is -0.05, perhaps a little surprising to me, I would have expected it slightly positive. But generally these correlations are between -0.25 and 0.25 in my experience, i.e. not very large.

[I left out the correlation between DAX and S&P: it is 0.725. Major world stock markets are always positively correlated].

Of course for a stock (as opposed to a stock index) the volatilities would be much higher (maybe double).

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  • $\begingroup$ So my recommendations are: the two stock volatilities shold be "big" and the currency volatility should be "small". The correlation between the two stock markets should be big and positive, the correlations of the currency to the stock markets can be of either sign but should be small in absolute value. $\endgroup$ – noob2 Feb 24 '17 at 15:21

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