Let's suppose USD/EUR price in USD follows a GBM with dSt=rStdt+σStdWt
What process does EUR/USD follow in EUR?
Answer
This will be the inverse process
1St
Applying Itô's formula the dynamics are then given by
d1St=−1S2tdSt+1S3tdStdSt
some simple algebra then leads to d1St=1St(σ2−r)dt+1StσdWt
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