Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. Join them; it only takes a minute:

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

Let's suppose USD/EUR price in USD follows a GBM with $$ dS_t = rS_tdt + \sigma S_tdW_t $$ What process does EUR/USD follow in EUR?

share|improve this question
up vote 2 down vote accepted

This will be the inverse process


Applying Itô's formula the dynamics are then given by

$$d\frac{1}{S_t}=\frac{-1}{S_t^2}dS_t+\frac{1}{S_t^3}dS_tdS_t$$ some simple algebra then leads to $$d\frac{1}{S_t}=\frac{1}{S_t}(\sigma^2 -r)dt+\frac{1}{S_t}\sigma dW_t$$

share|improve this answer
I think there should be -ve sign for the last term. – Quin Lai Nov 22 '14 at 20:05

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.