Do local banks allow you to borrow in currencies other than the local currency? If so, would the financing rate be different depending the currency?
It depends on the country-- there is no general answer. In some countries, it is common for loans to be available in the local currency or in some other currency. In others it is not. In Canada specifically, it's generally possible to get loans in either Canadian dollars or in US dollars.
In general, banks will charge different rates for loans in different currencies if only because different currencies have different levels of expected inflation. Of course, if the two currencies have roughly the same level of expected inflation, it is possible that at some moment in time the rates would be identical.
And, of course, if you have enough money, it's almost always possible to arrange a loan in whatever currency you want. A large bank would almost certainly find a way to loan Bill Gates several million dollars in whatever currency he wanted if he called up and asked even though that's not a service they'd offer John Doe walking in off the street into a branch.
Banks widely offer loans in BGN (the local currency), as well as in EUR and USD.
The interest rates for EUR and USD are somewhat lower than those for BGN. The difference used to be higher in the past.
Context: BGN is pegged to EUR at a fixed rate for 3 decades with no prospects of unpegging it at any point in time. It used to be fixed to DEM(Deutsche Mark) at 1:1 until DEM fused into EUR. Bulgaria is expected (if nothing breaks) to start using EUR at the start of 2024 and then gradually deprecate BGN for few years.
Even at a fixed rate, the risks are considered somewhat higher than those for EUR and USD.
Yes, but with caveats
Banks can do that and do that. It's far more common for commercial loans than for household consumption or housing loans.
The financing rate will be different, both because the interbank market interest rate is different for different currencies, and also because of the changes in risk - having a loan currency that's different from the currency of your income (usually but not always the local currency) creates an increased exposure to risk of default because if for some reason your income currency devaluates relative to the loan currency, then repaying the loan suddenly becomes more expensive, so banks may want to impose stricter repayment-to-income or loan-to-collateral ratios than for loans without such currency risk.
Two popular scenarios I've seen in the household lending business is lending in USD in non-USD countries where the local currencies are considered less stable, and at one point a decade or two ago housing loans denominated in CHF (Swiss Franc) were popular in some countries because CHF had a very low interest rate back when EUR rates were relatively higher, making it attractive for borrowers.
It was very common to get loans in either CHF, EUR or JPY, as these currencies had a much-much lower interest rate as HUF. To see how much: EUR morgages had an interest rate of around 4-5%, while HUF rates were much higher at 15-20%. CHF and JPY had even lower interest rates than EUR as well if I recall correctly.
When getting one of these loans you would see how much you had to repay every month in both the original currency and in HUF as well - this value was calculated based on the rates when you took out the loan. So on paper these loans usually looked much more affordable than a HUF based one. The fact that you had to repay the loan in the foreign currency was usually only marked in the Terms&Conditions, and of course most people never thought about that FX rates can deterioriate that much.
Also the idea was that - especially for loans in EUR - that as HUF would eventually be pegged to EUR, so it was a potentially low-risk option to get a much more beneficial interest rate. Do note people still got their salaries in HUF, and repayment was also done in HUF - the bank told you at the start of each month how much HUF you need to send in to cover the repayment amount, which was obviously set in the relevant foreign currency. For example if you took out a 1000 CHF loan and you had to repay it by sending 50 CHF every month, the bank would tell you at the start of the month how much 50 CHF is in HUF, and you had to deposit that amount.
This has caused a major problem around the 2008 recession when the value of HUF lost a lot against these other currencies. As an extreme example JPY/HUF was around 1.4 in 2008 but reached 3.0 in 2010. This means if you took out a JPY based loan in 2008, by 2010 your monthly repayments would have more than doubled! HUF also never got to be pegged to EUR, and is still free-floating as of 2022 on the FX market.
This has caused a lot of people to default on their loans - both because people lost their jobs because of the recessision and also because the monthly repayment amounts have skyrocketed when you looked at them from a HUF perspective.
To combat this the government first banned JPY and CHF based loans, then finally all non-HUF based ones around 2010 (with some exceptions - for example you could still get an EUR based mortgage if you could prove you got your salary in EUR). As a further measure the government in 2015 also mandated banks to convert all remaining loans that were still in non-HUF denominations to a HUF based loan. The govvernment also tried to push down HUF based interest rates to 4-5% or even lower to match the rates that were only possible using EUR based loans in the past.
This marked an abrupt end to non-HUF based loans in Hungary, and today you cannot get a non-HUF loan from a high street bank anymore (with some very-very strict exceptions)