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Position here is the residual amount of one or other currency at the end: You gave us: Time | Amount | Rate | t1 100 1.2636 t2 -1000 1.2599 t3 200 1.1612 Assuming the Amount is amount paid in USD, and the rate is EUR/USD: Time | Amount | Rate | EUR balance | USD balance t0 0 0 t1 ...

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Position means inventory. See Survey of market making strategies and research What you're puzzling about is what would be the value of your inventory in some risk (PnL) currency other than the currency you actually have. That's why you'd have rates from one currency to another. But the current value of your inventory expressed in terms of some other ...

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You aren't including how much of your base currency you have in your portfolio. Once you do that your position can be written as $X$ USD and $Y$ EUR. Beyond doing much of the work for your P&L computation, this is also useful for monitoring your risk to FX changes.

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