Hi all, Say one company is listed in 2 exchanges and they both have options on their exchange. One trades at 20% impl vol and another at 25% impl vol. Is there a way to arbritrage on this? Note that at the current FX, the prices are fair and we can't buy one/sell the other immediately to make profit. In the 'long run', should impl vol stay identical? (or is there a theory saying that if there's no immediate arbitrage oppurtunity, under certain condition/assumption, then the impl vol should automatically be the same, etc?)Thanks!

In stead of stocks lets assume this is EUR/USD and EUR/SEK. According to the BBA vols on May 31 where 9.03 and 3.34 respectively for the one month ATMF. There is "no" arbitrage between EUR/USD, USD/SEK and EUR/SEK. For our purpose, lets ignore interest-rates and assume they are constant and equal.We sell the EUR/USD and buy the EUR/SEK 0 delta straddles and get some money. But is it risk free?Next lets assume the market moves, the euro strengthens and we get a -1 delta on the EUR/USD and a 1 delta on the EUR/SEK (conveniently the same delta). Net we are long USD short SEK, and thus we have a market risk in USD/SEK.The point is, we have a correlation risk between the currency pairs.p.s. Quickly looking at the charts the above trade looks quite nice. To bad we don't have a time machine

Can we derive a formula with the fx random variable in there, with the 2 vols?

There is a simple mathmatical relationship between the vol of the stock in each currency, and the vol of the fx rate. And in 1991 you could find arbitrage opportunities! But nowadays there are hedge funds and prop trading desks that have computers that scan continuously looking for such an arbitrage and if an option contract gets out of line, *bang* a trade occurs and it is back to fair value.Let me tell you about a money losing trade I did on Sony ADR options vs Sony OTC common stock options. One was struck in USD and one was struck in JPY. A bit of analysis showed that something like 80% of Sony's profit stream was in USD, and the company admitted that they did relatively little FX hedging. You could see how much of their debt was denominated in USD, and your only conclusion was that this was a company whose profitability was strongly USD linked. Very much the same as Honda, in fact.Honda's ADR option vols were lower in USD than they were in JPY, which made sense. Honda are like a USD income stream. Therefore the stock vol would be lowest when measured in USD. When you value Honda in JPY you are actually adding in an FX vol (with correlation effect), so you expect a higher vol in JPY and you get it.But Sony's ADR option vols were significantly higher than the implied vols of the common stock, even though tis earnings were mostly USD denominated!Historical vols were around the same value with some fluctuation. OK - I had a fundamental story and historical data to back up the trade. After discussing the trade with a number of analysts I went short vol in the ADR options and long vol in the JPY stock options.The result? A random walk that ended slightly negative!My conclusion is that stocks can act in seemingly illogical ways for extended periods of time, regardles of fundamentals. There are easier ways to make money than in the ADR vs native currency option game!

how far out was the maturity of the trade? realized corr can always come and bite you in the ass..

Trade was roughly 1 year at inception. There were never any large PNL swings either way - it was just a boring random walk. I even delta hedged an FX option for awhile just in case some interesting things happened.You could perform all manner of anlysis - was it better to delta hedge each trade individually, or delta the whole mess with either common stock or ADRs?None of that mattered to any statistically significant degree. What it came down to is that the market mostly ignored the effect of USD moves on Sony's profitability!