An increase in the exchange rate S(€/$) has different effects on European currency options written on the euro with a strike price in dollars. Let's break down the effects separately for calls and puts:
1. Calls: An increase in the exchange rate (S(€/$)) benefits the holder of a call option. When the exchange rate increases, it means that each euro is worth more in dollars. As a result, the call option gives the holder the right to buy euros at a lower strike price in dollars. This leads to an increase in the value of the call option.
2. Puts: On the other hand, an increase in the exchange rate (S(€/$)) negatively impacts the holder of a put option. As the exchange rate increases, each euro becomes more valuable in dollars. This means that the put option, which gives the holder the right to sell euros at a higher strike price in dollars, becomes less valuable. Therefore, the value of the put option decreases.
So, to summarize:
- An increase in the exchange rate (S(€/$)) increases the value of call options.
- An increase in the exchange rate (S(€/$)) decreases the value of put options.
Remember that these effects hold true assuming all other factors remain constant (ceteris paribus).
In conclusion, an increase in the exchange rate S(€/$) has opposite effects on the value of European currency options written on the euro with a strike price in dollars. It increases the value of calls but decreases the value of puts.