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How does the change in FX volatility affect the counterparty risk of an FX-forward? Should it not be riskless since the forward itself is "protecting" the exchange rate fluctuations?

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I think the misunderstanding here is that the 'protection' that the FX Forward offers can turn into a counterparty risk in the end of the day.

To put it simply, if you lock for yourself a nice rate and the market moves downwards then are you sure that your counterparty will be able to pay you on the maturity date?

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At a general level it is helpful to delineate market (price) risk and counterparty credit risk.

And in terms of market risk, the FX forward protects you against unfavourable currency rate move at the delivery date.

Counteparty credit risk exists over the life of the contract whenever forward value is positive to your side. And, yes, the higher the currency rate volatilty, the higher the counteparty credit risk should be. If you proceeded to calculate credit risk profile you, then volatility would enter into a simulation model of the currency rate and higher parameter values would result in wider forward value distribution. Intuitively, probability that the contract will be extremely positive to your side is higher when the volatility is higher.

In reality things are more complicated when there is collaterisation scheme (as mentioned already), but you asked about a general relationship without further assumptions.

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Well yeah the whole point of an FX forward is to insure the counterparty from FX and interest rate risk. The future cashflows are fixed whatever the FX and interest rate volatility. However, since no cashflows actually take place until value date then to deal with counterparty risk then collateral is usually required. I think that's going to be a requirement in Mifid II

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