# Using Pint for currency conversions¶

Currency conversion tends to be substantially more complex than physical units. The exact exchange rate between two currencies:

• changes every minute,
• changes depending on the place,
• changes depending on who you are and who changes the money,
• may be not reversible, e.g. EUR->USD may not be the same as 1/(USD->EUR),
• different rates may apply to different amounts of money, e.g. in a BUY/SELL ledger,
• frequently involves fees, whose calculation can be more or less sophisticated. For example, a typical credit card contract may state that the bank will charge you a fee on all purchases in foreign currency of 1 USD or 2%, whichever is higher, for all amounts less than 1000 USD, and then 1.5% for anything in excess.

You may implement currencies in two ways, both of which require you to be familiar with Contexts.

## Simplified model¶

This model implies a few strong assumptions:

• There are no conversion fees
• All exchange rates are reversible
• Any amount of money can be exchanged at the same rate
• All exchanges can happen at the same time, between the same actors.

In this simplified scenario, you can perform any round-trip across currencies and always come back with the original money; e.g. 1 USD -> EUR -> JPY -> GBP -> USD will always give you 1 USD.

In reality, these assumptions almost never happen but can be a reasonable approximation, for example in the case of large financial institutions, which can use interbank exchange rates and have nearly-limitless liquidity and sub-second trading systems.

This can be implemented by putting all currencies on the same dimension, with a default conversion rate of NaN, and then setting the rate within contexts:

USD = [currency]
EUR = nan USD
JPY = nan USD
GBP = nan USD

@context FX
EUR = 1.11254 USD
GBP = 1.16956 EUR
@end


Note how, in the example above:

• USD is our base currency. It is arbitrary, only matters for the purpose of invoking to_base_units(), and can be changed with Different Unit Systems (and default units).
• We did not set a value for JPY - maybe because the trader has no availability, or because the data source was for some reason missing up-to-date data. Any conversion involving JPY will return NaN.
• We redefined GBP to be a function of EUR instead of USD. This is fine as long as there is a path between two currencies.

## Full model¶

If any of the assumptions of the simplified model fails, one can resort to putting each currency on its own dimension, and then implement transformations:

EUR = [currency_EUR]
GBP = [currency_GBP]

@context FX
GBP -> EUR: value * 1.11108 EUR/GBP
EUR -> GBP: value * 0.81227 GBP/EUR
@end

>>> q = ureg.Quantity("1 EUR")
>>> with ureg.context("FX"):
... q = q.to("GBP").to("EUR")
>>> q
0.9024969516 EUR


More sophisticated formulas, e.g. dealing with flat fees and thresholds, can be implemented with arbitrary python code by programmatically defining a context (see Contexts).