Of course the seller of the option needs to be compensated for giving such a right. The compensation is called the price or the premium of the option. Since the seller of the option is being compensated with the premium for giving the right, the seller thus has an obligation in the event the right is exercised by the buyer.
In hedging using options, calls are used if the risk is an upward trend in price and puts are used if the risk in a downward trend in price. In our Mr.A example, since the risk is a depreciation of Euro, Mr.A would need to buy put options on Euro. If Euro were to actually depreciate by the time Mr.A receives its Euro
revenue then Mr.A would exercise its right and exchange its Euro at the higher exercise rate. If however Euro were to appreciate instead, Mr.A would just let the contract expire and exchange its Euro in the spot market for the higher exchange rate. Therefore the options market allows traders to enjoy unlimited favourable movements while limiting losses. This feature is unique to options, unlike the forward or futures contracts where the trader has to forego favourable movements and there is also no limit to losses