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How does the value of an asset (valued in two different currencies) change when the exchange rate changes?
If there is a very sudden and large collapse in the exchange rate then because algorithmic trades will operate very fast it is possible to determine “x” immediately after the change in exchange rate. All you need to know is the order book. You also need to assume that the algorithmic bot operates faster than all other market participants so that the order book doesn’t change except for those trades executed by the bot. The temporarily cheaper price in the weakened currency market will rise and the temporarily dearer price in the strengthened currency market will fall until the prices are related by the new exchange rate. This price is determined by the condition that the total volume of buys in the cheaper market is equal to the total volume of sells in the dearer market.   Suppose initially gold is worth $1200 on NYSE or £720 on LSE. Then suppose the exchange rate falls from r=0.6 £/$ to s=0.4 £/$.  To illustrate the answer lets assume that before the currency collapse the order book for gold on the LSE and NYSE looks like: GOLD-NYSE   Sell (100 @ $1310) Sell (100 @ $1300) <——— Sell (100 @ $1280) Sell (200 @ $1260) Sell (300 @ $1220) Sell (100 @ $1200) ————————— buy (100 @ $1190) buy (100 @ $1180)   GOLD-LSE Sell (100 @ £750) Sell (100 @ £740) ————————— buy (200 @ £720) buy (200 @ £700) buy (100 @ £600) buy (100 @ £550) buy (100 @ £530) buy (100 @ £520) <——— buy (100 @ £500)   From this hypothetical example, the automatic traders will buy up the NYSE gold and sell the LSE gold in equal volume until the price ratio "s" is attained. By summing up the sell volumes on the NYSE and the buy volumes on the LSE, we see that the conditions are met when the price is $1300 and £520. Note 800 units were bought and sold.   So “x” depends on the available orders in the order book. Immediately after this, however, the price of the asset will be subject to the new changes of preference by the market participants. However, the price calculated above must be the initial price, since otherwise an arbitrage opportunity would exist.