Suppose an asset is traded on two different exchanges in different countries having different currencies. In an ideal world without transaction costs, tariffs, taxes or delivery costs etc, the price of the asset in the two markets, in equilibrium, should be equal after applying the exchange rate. If not, there would be a arbitrage opportunity. That is, one could make a risk free profit by buying the asset from the relative cheaper market (putting upward pressures on prices) and selling it back to the relatively more expensive market (putting downward pressure on prices) until the asset was priced equally-relative to the exchange rate in the two markets.
My question is this, let's assume we begin in this equilibrium situation. Now suppose that overnight the exchange rate experiences a drastic change. What will be the new equilibrium value of the asset in the two exchanges?
For concreteness, suppose that the "asset" is gold. Suppose that the markets are the US and the UK with the initial exchange rate, r=0.6 £/$. Initially the gold per ounce is worth A=$1200 dollars in the US and B=rA pounds in the UK. Then suddenly overnight the exchange rate changes to s, where s<< r. It is clear that eventually the asset will reach a new equilibrium value, say, $x dollars in the US and s*x pounds in the UK. What is x?
Applying the above arbitrage reasoning, immediately after the change in exchange rate, the product will be still worth $A dollars in the US and B=rA pounds in the UK. So if fast enough one could take sA pounds and convert them into $A dollars, then buy the gold from the US market and then sell it in the UK for £rA, receiving a risk free profit £(r-s)A. Clearly, if the markets were roughly the same size then this would put supply-demand pressures on both markets, so that the product value would rise in the US and fall in the UK. But by how much? What factors are important in order to work this out? Is the relative size of the two markets, the order book size, important in this calculation? I'm assuming that the markets are efficient in the sense that the price discovery that is due to the change in exchange rate is very fast.